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X-ORIGINAL-URL:https://ccg.ibs.re.kr
X-WR-CALDESC:Events for Center for Complex Geometry
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BEGIN:VTIMEZONE
TZID:Asia/Seoul
BEGIN:STANDARD
TZOFFSETFROM:+0900
TZOFFSETTO:+0900
TZNAME:KST
DTSTART:20210101T000000
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END:VTIMEZONE
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20221027T110000
DTEND;TZID=Asia/Seoul:20221027T120000
DTSTAMP:20221202T211124
CREATED:20220907T075418Z
LAST-MODIFIED:20221011T102020Z
UID:1701-1666868400-1666872000@ccg.ibs.re.kr
SUMMARY:Jaewoo Jeong\, Hankel Index of Smooth Non-ACM Curves of Almost Minimal Degree
DESCRIPTION: Speaker\n\n\nJaewoo Jeong IBS CCG\n\n\n\n\n \nThe Hankel index of a real variety is a semi-algebraic invariant that quantifies the (structural) difference between nonnegative quadrics and sums of squares on the variety. Note that the Hankel index of a variety is difficult to compute and was computed for just few cases. In 2017\, Blekherman\, Sinn\, and Velasco provided an captivating (lower) bound of the Hankel index of a variety by an algebraic invariant\, Green-Lazarsfeld index\, of the variety. In particular\, if the variety X is an arithmetrically Cohen-Macaulay (ACM) variety of almost minimal degree\, then the Hankel index of X equals to the Green-Lazarsfeld index of X plus one (which is the equality case of the bound). We study the Hankel index of smooth non-ACM curves of almost minimal degree. Note that the curve is the image of the projection of rational normal curves away from an outer point. It is known that the Green-Lazarsfeld index of the curve is determined by the rank of the center of the projection with respect to the rational normal curve. We found a new rank of the center that detects the Hankel index of the rational curves. In addition\, it turns out that the rational curves are the first class of examples that the lower bound of the Hankel index is strict.
URL:https://ccg.ibs.re.kr/event/2022-10-27/
LOCATION:B236-1\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20221013T110000
DTEND;TZID=Asia/Seoul:20221013T120000
DTSTAMP:20221202T211124
CREATED:20220830T070032Z
LAST-MODIFIED:20220928T015047Z
UID:1693-1665658800-1665662400@ccg.ibs.re.kr
SUMMARY:Jinhyun Park\, A Reciprocity Theorem Arising from a Family of Algebraic Curves
DESCRIPTION: Speaker\n\n\nJinhyun Park\nKAIST\n\n\n\n\n\n\nThe classical reciprocity theorem\, also called the residue theorem\, states that the sum of the residues of a rational (meromorphic) differential form on a compact Riemann surface is zero. Its generalization to smooth projective curves over a field is often called the Tate reciprocity theorem. \nThere is a different “multiplicative version” too. Here\, instead of a rational form\, one uses a pair of rational functions on a smooth projective curve\, and instead of residues\, one uses “Tame symbols”. The corresponding global result is called the Weil reciprocity. This result is elegantly reformulated in terms of the Milnor K-theory\, and it is generalized to sequences of rational functions by A. Suslin. This Suslin reciprocity was recently strengthened by D. Rudenko\, resolving a conjecture of A. Goncharov. \nIn this talk\, let me sketch my recent work in-progress\, that studies a different kind of reciprocity results coming from a proper family of algebraic curves over an algebraically closed field of characteristic 0.
URL:https://ccg.ibs.re.kr/event/2022-10-13/
LOCATION:B236-1\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220915T110000
DTEND;TZID=Asia/Seoul:20220915T120000
DTSTAMP:20221202T211124
CREATED:20220822T053515Z
LAST-MODIFIED:20220828T054540Z
UID:1677-1663239600-1663243200@ccg.ibs.re.kr
SUMMARY:Benjamin McMillan\, The Range of the Killing Operator
DESCRIPTION: Speaker\n\n\nBenjamin McMillan\nIBS-CCG\n\n\n\n\n\n\nThe Killing operator in (semi) Riemannian geometry has well understood kernel: the infinitesimal symmetries of a given metric. At the next level\, the range of the Killing operator can be interpreted as those perturbations of the metric that result from a mere change of coordinates—in contexts like general relativity\, the trivial perturbations. The range of the Killing operator\, albeit important\, has not been as well understood as its kernel. I will describe how one can use the projective nature of the Killing operator to reduce the question to that of the range of a connection on an associated bundle\, and then how one can seek to understand the range of an arbitrary connection. This process yields a fairly complete answer on locally symmetric spaces. \nBased on joint work with Federico Costanza\, Mike Eastwood\, and Thomas Leistner.
URL:https://ccg.ibs.re.kr/event/2022-09-15/
LOCATION:B236-1\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220901T110000
DTEND;TZID=Asia/Seoul:20220901T120000
DTSTAMP:20221202T211124
CREATED:20220822T053338Z
LAST-MODIFIED:20220822T065042Z
UID:1673-1662030000-1662033600@ccg.ibs.re.kr
SUMMARY:Guolei Zhong\, Dynamical Characterization of Projective Toric Varieties
DESCRIPTION: Speaker\n\n\nGuolei Zhong\nIBS-CCG\n\n\n\n\n\nAs a fundamental building block of the equivariant minimal model program\, the rationally connected variety plays a significant role in the classification of projective varieties admitting non-isomorphic endomorphisms. Twenty years ago\, Nakayama confirmed Sato’s conjecture that\, a smooth projective rational surface is toric if and only if it admits a non-isomorphic endomorphism. In this talk\, I will survey some recent progress on a higher dimensional analogue of Nakayama’s result. This talk is based on some joint works with Jia Jia\, Sheng Meng and De-Qi Zhang.
URL:https://ccg.ibs.re.kr/event/2022-09-01/
LOCATION:B266\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220324T162000
DTEND;TZID=Asia/Seoul:20220324T172000
DTSTAMP:20221202T211124
CREATED:20220304T075827Z
LAST-MODIFIED:20220304T075827Z
UID:1197-1648138800-1648142400@ccg.ibs.re.kr
SUMMARY:Hoseob Seo\, On L2 Extension from Singular Hypersurfaces
DESCRIPTION: Speaker\n\n\nHoseob Seo\nIBS CCG\n\n\n\n\n\nIn L2 extension theorems from an irreducible singular hypersurface in a complex manifold\, important roles are played by certain measures such as the Ohsawa measure\, which determines when a given function can be extended. In this talk\, we show that the singularity of the Ohsawa measure can be identified in terms of algebraic geometry.\nUsing this\, we give an analytic proof of the inversion of adjunction in this setting. These considerations enable us to compare various positive and negative results on L2 extension from singular hypersurfaces. In particular\, we generalize a recent negative result of Guan and Li which places limitations on strengthening such L2 extension by employing a less singular measure in the place of the Ohsawa measure. This is joint work with Dano Kim.
URL:https://ccg.ibs.re.kr/event/2022-03-24-1620/
LOCATION:B234
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220324T150000
DTEND;TZID=Asia/Seoul:20220324T160000
DTSTAMP:20221202T211124
CREATED:20220324T060000Z
LAST-MODIFIED:20220314T062449Z
UID:1200-1648134000-1648137600@ccg.ibs.re.kr
SUMMARY:Yonghwa Cho\, Nodal Sextics and Even Sets of Nodes
DESCRIPTION: Speaker\n\n\nYonghwa Cho\nIBS CCG\n\n\n\n\n\nIt is a classical question to ask how many nodes may a surface contain. For sextics\, the maximum number of nodes is 65\, and is attained by Barth’s example. We ask further: are all sextics with 65 nodes like Barth’s example? To find an answer\, we study even sets of nodes on sextic surfaces\, and prove that all sextics with 65 nodes share the same structure of even sets. This establishes a resemblance between Barth’s sextic and other sextics with 65 nodes. This talk is based on a joint work with Fabrizio Catanese\, Michael Kiermaier\, and Sascha Kurz.
URL:https://ccg.ibs.re.kr/event/2022-03-24-1500/
LOCATION:B234
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220303T162000
DTEND;TZID=Asia/Seoul:20220303T172000
DTSTAMP:20221202T211124
CREATED:20220207T112309Z
LAST-MODIFIED:20220207T112309Z
UID:1112-1646324400-1646328000@ccg.ibs.re.kr
SUMMARY:Guolei Zhong\, Strictly Nef Divisors on Singular Varieties
DESCRIPTION: Speaker\n\n\nGuolei Zhong\nIBS CCG\n\n\n\n\n\nA Q-Cartier divisor on a normal projective variety is said to be strictly nef\, if it has positive intersection with every integral curve. It has been a long history for people to measure how far a strictly nef divisor is from being ample. In this talk\, I will survey some recent progress on this topic\, especially the generalizations of Campana-Peternell’s conjecture and Serrano’s conjecture. My talk is based on some joint works with Jie Liu\, Wenhao Ou\, Juanyong Wang and Xiaokui Yang.
URL:https://ccg.ibs.re.kr/event/2022-03-03-1620/
LOCATION:TBA
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220303T150000
DTEND;TZID=Asia/Seoul:20220303T160000
DTSTAMP:20221202T211124
CREATED:20220303T060000Z
LAST-MODIFIED:20220214T022608Z
UID:1110-1646319600-1646323200@ccg.ibs.re.kr
SUMMARY:Luca Rizzi\, An Approach to the Fujita Decomposition via Massey Products and Castelnuovo-de Franchis Theorem
DESCRIPTION: Speaker\n\n\nLuca Rizzi\nIBS CCG\n\n\n\n\n\nLet f be a semistable fibration between a smooth complex variety of dimension n and a smooth complex curve. By a famous result of Fujita the direct image of the relative dualizing sheaf is the direct sum of a unitary flat vector bundle and an ample vector bundle. In this talk we focus our attention on the former: unitary flat bundles are in one-to-one correspondence with local systems and monodromy representations and I will show how these local systems are related to the de Rham closed one forms and top forms on the fibers of f. I will also give an introduction on the construction of Massey products and show its close relation with both a famous result by Castelnuovo and de Franchis and these local systems. Thanks to the presented techniques it is possible to give some results on the finiteness of the monodromy associated to the unitary flat bundle; equivalently on its semi-ampleness.
URL:https://ccg.ibs.re.kr/event/2022-03-03-1500/
LOCATION:TBA
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220224T110000
DTEND;TZID=Asia/Seoul:20220224T120000
DTSTAMP:20221202T211124
CREATED:20220224T020000Z
LAST-MODIFIED:20220126T041807Z
UID:1077-1645700400-1645704000@ccg.ibs.re.kr
SUMMARY:Jeong-Seop Kim\, Positivity of Tangent Bundles of Fano Threefolds
DESCRIPTION: Speaker\n\n\nJeong-Seop Kim\nKAIST\n\n\n\n\n\nAs well as the Hartshorne-Frankel conjecture on the ampleness of tangent bundle\, it has been asked to characterize a smooth projective variety X whose tangent bundle TX attains certain positivity\, e.g.\, nefness\, k-ampleness\, or bigness. But for the ampleness\, the complete answers are not known even within the class of smooth Fano varieties\, only partial answers are known in the case of lower dimension or lower Picard number\, some of which rely on classification theorems. On the bigness of TX\, the characterization has been done recently in the case of dimension 2 (Höring-Liu-Shao) and dimension 3 with Picard number 1 (Höring-Liu) using a special divisor on P(TX)\, called the total dual VMRT. In this talk\, I will briefly review the classification of Fano threefolds and the theory of total dual VMRT. Then I will introduce some criteria to determine the bigness of TX\, and announce a result on the bigness of TX in the case of dimension 3 with higher Picard number. This is joint work with Hosung Kim and Yongnam Lee.
URL:https://ccg.ibs.re.kr/event/2022-02-24/
LOCATION:TBA
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220210T110000
DTEND;TZID=Asia/Seoul:20220210T120000
DTSTAMP:20221202T211124
CREATED:20220210T020000Z
LAST-MODIFIED:20220124T121022Z
UID:1027-1644490800-1644494400@ccg.ibs.re.kr
SUMMARY:Young-Hoon Kiem\, A New Construction of the Moduli Space of Pointed Stable Curves of Genus 0
DESCRIPTION: Speaker\n\n\nYoung-Hoon Kiem\nSeoul National University\n\n\n\n\n\nThe moduli space of n points on a projective line up to projective equivalence has been a topic of research since the 19th century. A natural moduli theoretic compactification was constructed by Deligne and Mumford as an algebraic stack. Later\, Knudsen\, Keel\, Kapranov and others provided explicit constructions by sequences of blowups. The known inductive constructions of Knudsen and Keel however are rather inconvenient when one wants to compute the cohomology of the compactified moduli space as a representation space of its automorphism group because the blowup sequences are not equivariant. I will talk about a new inductive construction of the much studied moduli space from the perspective of sheaf theory. In fact\, we consider the moduli space of rank 1 stable pairs over the moduli space of n pointed stable curves of genus 0. By studing the wall crossing\, we obtain an equivariant sequence of blowups which ends up with the moduli space of n+1 pointed stable curves of genus 0. As an application\, we provide a closed formula of the character of the cohomology of the moduli space. We also provide a partial answer to a question of Manin and Orlov which asks whether the cohomology is a permutation representation or not. Based on a joint work with Jinwon Choi and Donggun Lee.
URL:https://ccg.ibs.re.kr/event/2022-02-10/
LOCATION:TBA
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220127T110000
DTEND;TZID=Asia/Seoul:20220127T120000
DTSTAMP:20221202T211124
CREATED:20220127T020000Z
LAST-MODIFIED:20220103T112105Z
UID:306-1643281200-1643284800@ccg.ibs.re.kr
SUMMARY:Jongbaek Song\, Regular Hessenberg Varieties and Toric Varieties
DESCRIPTION: Speaker\n\n\nJongbaek Song\nKIAS\n\n\n\n\n\nA Hessenberg variety is a subvariety of the flag variety (G/B) determined by two parameters: one is an element of the Lie algebra of G and the other is a B-submodule containing the Lie algebra of B\, known as a Hessenberg space. In this talk\, we focus on elements in the regular locus of the Lie algebra and the Hessenberg space determined by negative simple roots. Then\, we aim to figure out cohomological relationship of these Hessenberg varieties with a certain class of toric varieties having orbifold singularities. The main result raises an interesting topic concerning toric varieties with symmetries by reflections. This is a joint work with M. Masuda\, T. Horiguchi and J. Shareshian.
URL:https://ccg.ibs.re.kr/event/2022-01-27/
LOCATION:TBA
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220120T110000
DTEND;TZID=Asia/Seoul:20220120T120000
DTSTAMP:20221202T211124
CREATED:20220120T020000Z
LAST-MODIFIED:20211227T043533Z
UID:991-1642676400-1642680000@ccg.ibs.re.kr
SUMMARY:Han-Bom Moon\, Derived Category of Moduli of Vector Bundles II
DESCRIPTION: Speaker\n\n\nHan-Bom Moon\nFordham University\n\n\n\n\n\nThe derived category of a smooth projective variety is an object expected to encode much birational geometric information. Recently\, there have been many results on decomposing derived categories into simpler building blocks. In the first lecture\, I will provide an elementary introduction to two independent topics — 1. the definition and basic properties of the derived category and 2. moduli spaces of vector bundles on a curve. In the second lecture\, I will present recent progress on the structure of the derived category of the moduli space. Most of the lectures will be accessible to graduate students with basic knowledge of algebraic geometry. The second lecture is based on ongoing joint work with Kyoung-Seog Lee.
URL:https://ccg.ibs.re.kr/event/2022-01-20/
LOCATION:TBA
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220119T100000
DTEND;TZID=Asia/Seoul:20220119T120000
DTSTAMP:20221202T211124
CREATED:20220119T010000Z
LAST-MODIFIED:20211227T043507Z
UID:910-1642586400-1642593600@ccg.ibs.re.kr
SUMMARY:Han-Bom Moon\, Derived Category of Moduli of Vector Bundles I
DESCRIPTION: Speaker\n\n\nHan-Bom Moon\nFordham University\n\n\n\n\n\nThe derived category of a smooth projective variety is an object expected to encode much birational geometric information. Recently\, there have been many results on decomposing derived categories into simpler building blocks. In the first lecture\, I will provide an elementary introduction to two independent topics — 1. the definition and basic properties of the derived category and 2. moduli spaces of vector bundles on a curve. In the second lecture\, I will present recent progress on the structure of the derived category of the moduli space. Most of the lectures will be accessible to graduate students with basic knowledge of algebraic geometry. The second lecture is based on ongoing joint work with Kyoung-Seog Lee.
URL:https://ccg.ibs.re.kr/event/2022-01-19/
LOCATION:TBA
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20211228T160000
DTEND;TZID=Asia/Seoul:20211228T170000
DTSTAMP:20221202T211124
CREATED:20211228T070000Z
LAST-MODIFIED:20211228T111500Z
UID:919-1640707200-1640710800@ccg.ibs.re.kr
SUMMARY:Paul-Andi Nagy\, Einstein Deformations of Hyperkaehler Cones
DESCRIPTION: Speaker\n\n\nPaul-Andi Nagy\nIBS CCG\n\n\n\n\n\nFor a hyperkaehler cone with compact link (M\, g) we describe the Einstein deformation theory of g and relate it to the algebraic geometry of the twistor space Z of M. This is joint work with Uwe Semmelmann.
URL:https://ccg.ibs.re.kr/event/2021-12-28-1600/
LOCATION:B236\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20211202T110000
DTEND;TZID=Asia/Seoul:20211202T120000
DTSTAMP:20221202T211124
CREATED:20211202T020000Z
LAST-MODIFIED:20211123T040520Z
UID:883-1638442800-1638446400@ccg.ibs.re.kr
SUMMARY:Sai-Kee Yeung\, Almost Complex Structures and Complex Structures on Manifolds of Even Dimension at Least 6
DESCRIPTION: Speaker\n\n\nSai-Kee Yeung\nPurdue University\n\n\n\n\n\nWe would like to explain for each real even dimension 2n ≥ 6 some examples of compact differentiable manifolds supporting an almost complex structure which cannot be deformed to an integrable complex structure.
URL:https://ccg.ibs.re.kr/event/2021-12-02/
LOCATION:on-line
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20211104T110000
DTEND;TZID=Asia/Seoul:20211104T120000
DTSTAMP:20221202T211124
CREATED:20211014T053459Z
LAST-MODIFIED:20211014T053459Z
UID:797-1636023600-1636027200@ccg.ibs.re.kr
SUMMARY:Jie Liu\, Bigness of Tangent Bundles of Fano Manifolds with Zero Dimensional VMRT
DESCRIPTION: Speaker\n\n\nJie Liu\nInstitute of Mathematics\, AMSS\, CAS\n\n\n\n\n\n\nIt is expected that the bigness of tangent bundle is a quite restrictive property for Fano manifolds\, especially for those of Picard number one. In this talk\, I will present our recent first attempt to tackle this problem. More precise\, we will consider Fano manifolds of Picard number one and having zero-dimensional VMRT\, and it turns out that in this case only the quintic del Pezzo threefold has big tangent bundle. This is based on my recent joint work with Andreas Höring.
URL:https://ccg.ibs.re.kr/event/2021-11-04/
LOCATION:TBA
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20211028T110000
DTEND;TZID=Asia/Seoul:20211028T120000
DTSTAMP:20221202T211124
CREATED:20211028T020000Z
LAST-MODIFIED:20211006T051155Z
UID:790-1635418800-1635422400@ccg.ibs.re.kr
SUMMARY:Feng Shao\, The Bigness of Tangent Bundles of Projective Manifolds
DESCRIPTION: Speaker\n\n\nFeng Shao\nIBS\, Center for Complex Geometry\n\n\n\n\n\n\nLet X be a Fano manifold. While the properties of the anticanonical divisor –KX and its multiples have been studied by many authors\, the positivity of the tangent bundle TX is much more elusive. In this talk\, we give a complete characterization of the pseudoeffectivity and the bigness of TX for del Pezzo surfaces\, hypersurfaces in the projective space and del Pezzo threefolds.
URL:https://ccg.ibs.re.kr/event/2021-10-28/
LOCATION:TBA
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20211014T110000
DTEND;TZID=Asia/Seoul:20211014T120000
DTSTAMP:20221202T211124
CREATED:20211014T020000Z
LAST-MODIFIED:20211005T030302Z
UID:787-1634209200-1634212800@ccg.ibs.re.kr
SUMMARY:Yewon Jeong\, Several Types of Dual Defective Cubic Hypersurfaces
DESCRIPTION: Speaker\n\n\nYewon Jeong\nIBS\, Center for Complex Geometry\n\n\n\n\n\n\nGiven a hypersurface X = V(f) in a complex projective space\, we say X is dual defective if the Gauss map of X\, the restriction of the gradient map of f on X\, has positive dimensional fibers. Especially for cubics\, there is an interesting classification of them. We will study several types of dual defective cubic hypersurfaces and the relation between them.
URL:https://ccg.ibs.re.kr/event/2021-10-14/
LOCATION:TBA
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210819T110000
DTEND;TZID=Asia/Seoul:20210819T120000
DTSTAMP:20221202T211124
CREATED:20210819T020000Z
LAST-MODIFIED:20210803T072832Z
UID:643-1629370800-1629374400@ccg.ibs.re.kr
SUMMARY:Sung Rak Choi\, Subadditivity of Okounkov Bodies
DESCRIPTION: Speaker\n\n\nSung Rak Choi\nYonsei University\n\n\n\n\n\n\nWe will investigate the subadditivity theorem of Okounkov bodies for algebraic fiber spaces. As an application\, we obtain the subadditivity of the numerical Kodaira dimension and the restricted volume for algebraic fiber spaces. As a byproduct\, we obtain a criterion of birational isotriviality in terms of Okounkov bodies when the general fiber is of general type. As a special case\, we prove some variants of the Iitaka conjecture. We expect that our results will provide a new approach toward the Iitaka conjecture. \nThis is an ongoing research\, in collaboration with Dr. Jinhyung Park.
URL:https://ccg.ibs.re.kr/event/2021-08-19/
LOCATION:on-line
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210812T110000
DTEND;TZID=Asia/Seoul:20210812T120000
DTSTAMP:20221202T211124
CREATED:20210812T020000Z
LAST-MODIFIED:20210803T072821Z
UID:641-1628766000-1628769600@ccg.ibs.re.kr
SUMMARY:Jinhyung Park\, Comparing Numerical Iitaka Dimensions
DESCRIPTION: Speaker\n\n\nJinhyung Park\nSogang University\n\n\n\n\n\n\nThere are several definitions of the “numerical” Iitaka dimensions of a pseudoeffective divisor\, which are numerical analogues to the Iitaka dimension. Recently\, Lesieutre proved that notions of numerical Iitaka dimensions do not coincide. In this talk\, we prove that many of numerical Iitaka dimensions are equal to the notion introduced by Boucksom-Demailly-Paun-Peternell and that some other invariants introduced by Nakayama and Lehmann can be arbitrarily larger than this notion. We also show some properties of abundant divisors. This is joint work with Sung Rak Choi.
URL:https://ccg.ibs.re.kr/event/2021-08-12/
LOCATION:on-line
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210708T140000
DTEND;TZID=Asia/Seoul:20210708T150000
DTSTAMP:20221202T211124
CREATED:20210622T042954Z
LAST-MODIFIED:20210628T125100Z
UID:608-1625752800-1625756400@ccg.ibs.re.kr
SUMMARY:Yonghwa Cho\, Cohomology of Divisors on Burniat Surfaces
DESCRIPTION: Speaker\n\n\nYonghwa Cho\nKIAS\n\n\n\n\n\n\nA (primary) Burniat surface is a complex surface of general type that can be obtained as a bidouble cover of del Pezzo surface with K2 = 6. The Picard group is an abelian group of rank 4 with torsion part isomorphic to (Z/2)6. Alexeev studied the divisors on Burniat surfaces\, and observed that the irreducible components of ramification divisors span the semigroup of effective divisors. Based on Alexeev’s result\, I will describe the method for computing cohomology of arbitrary divisors on Burniat surfaces. If time permits\, (non-)existence question about Ulrich bundles will be discussed as an application.
URL:https://ccg.ibs.re.kr/event/2021-07-08-1400/
LOCATION:B266\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210708T110000
DTEND;TZID=Asia/Seoul:20210708T120000
DTSTAMP:20221202T211124
CREATED:20210622T042608Z
LAST-MODIFIED:20210622T042608Z
UID:605-1625742000-1625745600@ccg.ibs.re.kr
SUMMARY:Sukmoon Huh\, Logarithmic Sheaves on Projective Surfaces
DESCRIPTION: Speaker\n\n\nSukmoon Huh\nSungkyunkwan University\n\n\n\n\n\n\nA logarithmic sheaf is a sheaf of differential one-forms on a variety with logarithmic poles along a given divisor. One of the main problems on this object is to see whether Torelli property holds\, i.e. whether two different divisors define two non-isomorphic logarithmic sheaves. In this talk\, after reviewing some basic material\, we are going to introduce two new approaches to obtain Torelli property. This is a joint work in progress with S. Marchesi\, J. Pons-Llopis and J. Valles.
URL:https://ccg.ibs.re.kr/event/2021-07-08/
LOCATION:B266\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210701T110000
DTEND;TZID=Asia/Seoul:20210701T120000
DTSTAMP:20221202T211124
CREATED:20210622T042251Z
LAST-MODIFIED:20210623T042117Z
UID:601-1625137200-1625140800@ccg.ibs.re.kr
SUMMARY:Yong Hu\, Noether-Severi Inequality and Equality for Irregular Threefolds of General Type
DESCRIPTION: Speaker\n\n\nYong Hu\nKIAS\n\n\n\n\n\n\nFor complex smooth irregular 3-folds of general type\, I will introduce the optimal Noether-Severi inequality. This answers an open question of Zhi Jiang in dimension three. Moreover\, I will also completely describe the canonical models of irregular 3-folds attaining the Noether-Severi equality. This is a joint work with Tong Zhang.
URL:https://ccg.ibs.re.kr/event/2021-07-01/
LOCATION:B266\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210617T110000
DTEND;TZID=Asia/Seoul:20210617T120000
DTSTAMP:20221202T211124
CREATED:20210520T034412Z
LAST-MODIFIED:20210615T082915Z
UID:504-1623927600-1623931200@ccg.ibs.re.kr
SUMMARY:Baohua Fu\, Normalized Tangent Bundle\, Pseudoeffective Cone and Varieties with Small Codegree
DESCRIPTION: Speaker\n\n\nBaohua Fu\nChinese Academy of Science\n\n\n\n\n\n\nWe propose a conjectural list of Fano manifolds of Picard number one whose normalized tangent bundle is pseudoeffective and we prove it in various situations by relating it to the complete divisibility conjecture of Russo and Zak on varieties with small codegrees. The pseudoeffective cone of the projectivized tangent bundle of a rational homogeneous space of Picard number one is explicitly determined by studying the total dual VMRT and the geometry of stratified Mukai flops. This is a joint work with Jie LIU.
URL:https://ccg.ibs.re.kr/event/2021-06-17/
LOCATION:on-line
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210603T110000
DTEND;TZID=Asia/Seoul:20210603T120000
DTSTAMP:20221202T211124
CREATED:20210518T033401Z
LAST-MODIFIED:20210518T033401Z
UID:496-1622718000-1622721600@ccg.ibs.re.kr
SUMMARY:Joonyeong Won\, K-stability\, Kähler-Einstein Metric on Fano Varieties and Sasaki-Einstein Metric on 5-dimensional Smale Manifolds
DESCRIPTION: Speaker\n\n\nJoonyeong Won\nKIAS\n\n\n\n\n\n\nWe discuss on recent progresses of the existence problem of Kähler-Einstein metric on Fano varieties by K-stability of them and also the existence problem of Sasaki-Einstein metric on 5-dimensional Smale manifolds via K-stability of weighted hypersurface log del Pezzo surfaces.
URL:https://ccg.ibs.re.kr/event/2021-06-03/
LOCATION:B266\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210527T110000
DTEND;TZID=Asia/Seoul:20210527T120000
DTSTAMP:20221202T211124
CREATED:20210430T040608Z
LAST-MODIFIED:20210430T042430Z
UID:443-1622113200-1622116800@ccg.ibs.re.kr
SUMMARY:Lucas Kaufmann\, Commuting Pairs of Endomorphisms
DESCRIPTION: Speaker\n\n\nLucas Kaufmann\nIBS\, Center for Complex Geometry\n\n\n\n\n\n\nThe study of functional equations is at the origin of the early developments of the iteration theory of polynomials and rational functions\, carried out by Fatou\, Julia\, Ritt and others. Among these equations\, the commutation relation f g = g f is particularly interesting. In this talk I will discuss the following problem: can we classify commuting pairs of holomorphic endomorphisms of the complex projective space? \nWe will see that the relation f g = g f gives rise to special symmetries of several dynamical objects attached to these maps\, such as their invariant currents and measures\, their Julia sets and so on. This rigidity allows us to understand the structure of these maps and even give a full description in low dimensions.
URL:https://ccg.ibs.re.kr/event/2021-05-27/
LOCATION:B266\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210520T110000
DTEND;TZID=Asia/Seoul:20210520T120000
DTSTAMP:20221202T211124
CREATED:20210430T040140Z
LAST-MODIFIED:20210430T042439Z
UID:437-1621508400-1621512000@ccg.ibs.re.kr
SUMMARY:Lucas Kaufmann\, Introduction to Dynamics in Several Complex Variables
DESCRIPTION: Speaker\n\n\nLucas Kaufmann\nIBS\, Center for Complex Geometry\n\n\n\n\n\n\nThe field of complex dynamics deals with the study of the iteration of a map from a complex manifold to itself. The one dimensional theory is more than one-hundred years old and is now very well developed. \nDue to the fundamental differences between complex analysis in one and higher dimensions\, the study of higher dimensional dynamical systems is much more recent and is still an active research domain\, with interesting connections to complex geometry\, algebraic geometry\, number theory\, mathematical physics etc. \nThe aim of this talk is to survey standard results on the dynamics of self-maps in complex manifolds. I will focus on the case of endomorphisms of the complex projective space and use it to illustrate how the tools of pluripotential theory and the theory of currents are crucial in their study. \nIn particular\, I aim to talk about Green currents and measures\, equidistribution theorems and\, if time permits\, relations with the intersection theory of currents.
URL:https://ccg.ibs.re.kr/event/2021-05-20/
LOCATION:B266\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210513T110000
DTEND;TZID=Asia/Seoul:20210513T120000
DTSTAMP:20221202T211124
CREATED:20201120T045532Z
LAST-MODIFIED:20210430T041419Z
UID:216-1620903600-1620907200@ccg.ibs.re.kr
SUMMARY:Jeong-Seop Kim\, Stability of Symmetric Powers of Vector Bundles on a Curve
DESCRIPTION: Speaker\n\n\nJeong-Seop Kim\nKAIST\n\n\n\n\n\nFor a stable vector bundle E on a smooth projective curve\, it is known that the symmetric powers Sk E are semi-stable and are stable for all k > 0 in sufficiently general. Moreover\, if E has rank 2\, then Sk E is destabilized by a line subbundle if and only if the ruled surface PC(E) admits a k-section of zero self-intersection. In this talk\, concentrating on the case of rank 2\, we will find answers to the questions of which E has strictly semi-stable Sk E\, and how many such E there are. Also\, we will introduce relations between such E and the orthogonal bundles when k = 2\, and Nori’s finite bundles when k ≥ 3.
URL:https://ccg.ibs.re.kr/event/2020-12-17/
LOCATION:B266\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210422T110000
DTEND;TZID=Asia/Seoul:20210422T120000
DTSTAMP:20221202T211124
CREATED:20210312T041646Z
LAST-MODIFIED:20210430T041501Z
UID:341-1619089200-1619092800@ccg.ibs.re.kr
SUMMARY:Hosung Kim\, The Space of Rational Curves on a General Hypersurface of Projective Space
DESCRIPTION: Speaker\n\n\nHosung Kim\nIBS\, Center for Complex Geometry\n\n\n\n\n\nIn 1979\, the work of Mori had brought out the importance of the study of rational curves in higher-dimensional geometry. In 1990s\, applying Mori’s bend-and-break method\, Campana and Kollar-Miyaoka-Mori proved that any Fano manifold is rationally connected. Since then the family of raional curves on Fano maniflolds has been considerably studied especially about the dimension and irreducibility. The expected dimension of the family of rational curves of degree e in a hypersurface of degree d in Pn is e(n-d+1)+n-4\, and it has been conjectured that this family is irreducible and has dimension of the expected dimension if d ≤ n-1 and n > 3. This conjecture has been proven for d ≤ n-2 and e arbitrary by Riedl and Yang in 2019 based on bend-and-break. For d = n-1\, some results for low e were obtained by Tseng in 2017. In this seminar I am going to introduce a technique based on degenerating the ambient projective space to a 2-component fan and simultaneously degenerate a general hypersurface of a projective space to a subscheme of the fan. Using this method\, Ziv Ran reduced the original problem to that on the space of rational curves in Pn which are some secant to a certain (d\,d-1) complete intersection\, and proved the cases when e < d ≤ n-1 and n > 4.
URL:https://ccg.ibs.re.kr/event/2021-04-22/
LOCATION:B266\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210415T110000
DTEND;TZID=Asia/Seoul:20210415T120000
DTSTAMP:20221202T211124
CREATED:20210312T042356Z
LAST-MODIFIED:20210430T041530Z
UID:348-1618484400-1618488000@ccg.ibs.re.kr
SUMMARY:Seungjae Lee\, L2 Extension of Holomorphic Jets on Complex Hyperbolic Forms
DESCRIPTION: Speaker\n\n\nSeungjae Lee\nIBS\, Center for Complex Geometry\n\n\n\n\n\nAs the continuation of the previous talk\, I discuss an L2 extension problem of holomorphic jets on compact complex hyperbolic forms. Let Γ be a cocompact torsion-free lattice in the automorphism group Aut(Bn) and Ω be a quotient Bn × Bn given by diagonal action of Γ. In the setting\, Ω becomes a ball-fiber bundle over Σ = Bn / Γ. Since we can identify symmetric differentials on Σ and jets of holomorphic function on D which is the maximal compact analytic variety on Ω\, it is natural to expect that holomorphic function on Ω can be derived by symmetric differentials. In this context\, M. Adachi (2017) extends holomorphic jets on D to weighted L2 holomorphic functions on Σ for the n=1 case. In 2020\, A. Seo and S. Lee generalized his result by developing a Hodge type identity on SmTΣ*. In this talk\, I will explain recent progress and if time is permitted\, I sketch the proof of our result. This is joint work with A. Seo.
URL:https://ccg.ibs.re.kr/event/2021-04-15/
LOCATION:B266\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
END:VEVENT
END:VCALENDAR