복소기하학연구단
Speaker Yoonjoo Kim Columbia U. I would like to report two ongoing results on Lagrangian fibrations of smooth symplectic varieties. The first is the construction of a delta-regular smooth group scheme that acts on a given Lagrangian fibration. It is a generalization of the result of Arinkin-Fedorov, who proved the result under the …
Speaker Makoto Enokizono University of Tokyo Noether-Horikawa surfaces are surfaces of general type satisfying the equation K2=2pg−4, which represents the equality of the Noether inequality K2≥2pg−4 for surfaces of general type. In the 1970s, Horikawa conducted a detailed study of smooth Noether-Horikawa surfaces, providing a classification of these surfaces and describing their moduli spaces. …
Speaker Doyoung Choi KAIST / IBS We study the higher secant varieties of a smooth projective variety embedded in projective space. We prove that when the variety is a surface and the embedding line bundle is sufficiently positive, these varieties are normal with Du Bois singularities and the syzygies of their defining ideals …
Speaker Haesong Seo KAIST / IBS A projective manifold is called hyperbolic if it does not admit an entire map from the complex plane. Demailly proved that hyperbolic manifolds are algebraically hyperbolic, meaning that there are degree bounds for curves in terms of their genera. It is a highly challenging problem to determine …
Speaker Minseong Kwon Gyeongsang National University In the 1970s, Demazure studied the automorphism groups of two types of almost homogeneous varieties: rational homogeneous spaces and toric varieties. Especially, for a smooth complete toric variety, Demazure obtained a structure theorem for the connected automorphism group in terms of the so-called Demazure roots. In this …
Speaker Gebhard Martin University of Bonn The automorphism group of a general Enriques surface is the 2-congruence subgroup of the Weyl group of the E10-lattice. In particular, it is infinite and not virtually solvable. On the other end of the spectrum, there do exist Enriques surfaces with finite automorphism group, first classified over …
Speaker Kyoung-Seog Lee POSTECH Intersections of two quadrics form an interesting class of algebraic varieties and they have been intensively studied from various aspects. In these talks, I will discuss these various aspects of the intersection of two quadrics and how to interpret/generalize some of the classical algebraic geometry results using the derived …
Speaker Kyoung-Seog Lee POSTECH Intersections of two quadrics form an interesting class of algebraic varieties and they have been intensively studied from various aspects. In these talks, I will discuss these various aspects of the intersection of two quadrics and how to interpret/generalize some of the classical algebraic geometry results using the derived …
Speaker Yen-An Chen KIAS For Fano varieties, significant progress has been made recently in the study of K-stability, while the understanding of the weaker but more algebraic concept of $(−K)$-slope stability remains intricate. For instance, a conjecture attributed to Iskovskikh states that the tangent bundle of a Picard rank one Fano manifold is …
Speaker Taiki Takatsu Tokyo University of Science We will discuss Mukai’s conjecture that the virtual cohomological dimension of the automorphism group of a K3 surface is equal to the maximum rank of its Mordell-Weil groups. The action of the automorphism group on the second cohomology induces a natural action on a hyperbolic space. …
Speaker Dae-Won Lee Ewha Womans University The study of cylinders in normal projective varieties is of significant interest due to their intrinsic link to unipotent group actions on affine algebraic varieties. Over a field $\mathbb{k}$ of characteristic zero, it is known that cylindricity in lower-dimensional varieties (appearing as generic fibers) implies the existence …
Speaker Dae-Won Lee Ewha Womans University This talk provides a brief survey of recent results and applications concerning the anticanonical minimal model program. Furthermore, we present examples of varieties that admit an anticanonical minimal model despite not being Mori dream spaces. This talk is based on joint work with Sung Rak Choi, Sungwook …