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X-WR-CALDESC:Events for Center for Complex Geometry
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TZID:Asia/Seoul
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DTSTART:20200101T000000
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210401T110000
DTEND;TZID=Asia/Seoul:20210401T120000
DTSTAMP:20260616T123555
CREATED:20210312T041527Z
LAST-MODIFIED:20210430T041721Z
UID:339-1617274800-1617278400@ccg.ibs.re.kr
SUMMARY:Qifeng Li\, Rigidity of Wonderful Group Compactifications under Fano Deformations
DESCRIPTION:     Speaker\n\n\nQifeng Li\nIBS\, Center for Complex Geometry\n\n\n\n\n\nFor a complex connected semisimple linear algebraic group G of adjoint type and of rank n\, De Concini and Procesi constructed its wonderful compactification X\, which is a smooth Fano variety of Picard number n enjoying many interesting properties. In this talk\, we will show that the wonderful compactification X is rigid under Fano deformations. Namely\, for any family of smooth Fano varieties over a connected base\, if one fiber is isomorphic to X\, then so are all other fibers. This answers a question raised by Bien and Brion in their work on the local rigidity of wonderful varieties.
URL:https://ccg.ibs.re.kr/event/2021-04-01/
LOCATION:B266\, IBS\, Korea\, Republic of
CATEGORIES:Complex Geometry Seminar
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210407T160000
DTEND;TZID=Asia/Seoul:20210407T180000
DTSTAMP:20260616T123555
CREATED:20210317T024334Z
LAST-MODIFIED:20210430T041731Z
UID:384-1617811200-1617818400@ccg.ibs.re.kr
SUMMARY:Jihun Yum\,  Characterization of Diederich-Fornaess and Steinness Indices in Complex Manifolds
DESCRIPTION:     Speaker\n\n\nJihun Yum\nIBS\, Center for Complex Geometry\n\n\n\n\n\n\nLet Ω be a relatively compact pseudoconvex domain in a complex manifold X with smooth boundary ∂Ω. The Diederich-Fornaess index and the Steinness index of Ω are defined by \nDF(Ω) := supρ { 0 < η < 1 : -(-ρ)η is strictly plurisubharmonic on Ω ∩ U for some neighborhood U of ∂Ω }\, \nS(Ω) := infρ { η > 1 : ρη is strictly plurisubharmonic on Ωc ∩ U for some neighborhood U of ∂Ω }\, \nwhere ρ is a defining function for Ω. \nIn the previous talk\, we have seen that two indices are completely characterized by D’Angelo 1-form when the ambient space is X = Cn. In this talk\, we generalize the formulas for a relatively compact pseudoconvex domains in a (general) complex manifold X. Since the formulas do not hold anymore in general\, unfortunately\, we introduce 4 kinds of each of the Diederich-Fornaess and Steinness indices. Then we give some non-degeneracy conditions for these indices agree. Also\, we exam the geometric meaning of the D’Angelo 1-form when the boundary ∂Ω is Levi-flat.
URL:https://ccg.ibs.re.kr/event/2021-04-07/
LOCATION:B266\, IBS\, Korea\, Republic of
CATEGORIES:Several Complex Variables Seminar
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210408T110000
DTEND;TZID=Asia/Seoul:20210408T120000
DTSTAMP:20260616T123555
CREATED:20210226T055225Z
LAST-MODIFIED:20210430T041740Z
UID:312-1617879600-1617883200@ccg.ibs.re.kr
SUMMARY:Seungjae Lee\, Symmetric Differentials on Complex Hyperbolic Forms
DESCRIPTION:     Speaker\n\n\nSeungjae Lee\nIBS\, Center for Complex Geometry\n\n\n\n\n\nLet Γ be a cocompact torsion-free lattice in the automorphism group of complex unit ball Bn\, Aut(Bn). In this talk\, we discuss the existence of symmetric differentials on the compact ball quotient Σ = Bn / Γ. Since Σ has a Kähler metric induced by the Bergman metric on the complex unit ball Bn\, it has symmetric differentials on SmTΣ* if m is sufficiently large. Unfortunately\, finding the smallest degree m which guarantees a symmetric differential on SmTΣ* is difficult in even compact ball quotient cases. Instead of this\, I will prove that m ≥ n+2 is a sufficient condition to give a symmetric differential on SmTΣ*. To achieve this goal\, I will explain how to induce symmetric differentials by using a recursive formula for ∂-operators and Poincaré series. This is joint work with A. Seo.
URL:https://ccg.ibs.re.kr/event/2021-04-08/
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:20260616T123555
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
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DTSTART;TZID=Asia/Seoul:20210421T160000
DTEND;TZID=Asia/Seoul:20210421T170000
DTSTAMP:20260616T123555
CREATED:20210409T050246Z
LAST-MODIFIED:20210430T041516Z
UID:417-1619020800-1619024400@ccg.ibs.re.kr
SUMMARY:Taeyong Ahn\, Positive Closed Currents and Super-potentials
DESCRIPTION:     Speaker\n\n\nTaeyong Ahn\nInha University\, Department of Mathematics Education\n\n\n\n\n\nIn this talk\, we briefly review the notion and properties of positive closed currents and super-potentials. As an application\, we discuss the equidistribution of positive closed currents on the projective space. We also discuss the difficulty of the extension of the result to a general compact Kähler manifold.
URL:https://ccg.ibs.re.kr/event/2021-04-21/
LOCATION:B266\, IBS\, Korea\, Republic of
CATEGORIES:Several Complex Variables Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210422T110000
DTEND;TZID=Asia/Seoul:20210422T120000
DTSTAMP:20260616T123555
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
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