복소기하학연구단
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 Jong Taek Cho Chonnam National University We survey recent developments of pseudo-Hermitian geometry or CR geometry of hypersurface type, with a particular focus on their symmetries and realizations as real hypersurfaces in Hermitian symmetric spaces.
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 Sui-Chung Ng ECNU A complex algebraic surface is called an elliptic surface if it is a fiber surface whose general fibers are elliptic curves. An elliptic surface can also be regarded as an elliptic curve $E$ over the function field $K$ of an algebraic curve. The holomorphic sections of that elliptic surface …
Speaker Yun Gao Shanghai Jiao Tong U Hilbert's 17-th problem asked whether a non-negative polynomial in several real variables must be a sum of squares of rational functions. There is also a quantitative version of Hilbert's 17th problem which asks how many squares are needed. D'Angelo extend this problem to more general case …
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 Katharina Neusser Masaryk University A cone structure on a manifold $M$ is given by a closed submanifold $\mathcal C\subset \mathbb P TM$ of the projectived tangent bundle of $M$, which is submersive over $M$. Such geometric structures arise naturally in differential and algebraic geometry and they come often equipped with a conic …
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 …