복소기하학연구단
Speaker Zhi Jiang SCMS, Fudan University Syzygies of ample line bundles on abelian varieties have attracted lots of attentions in recent years. People tried to study these geometric objects by different methods, including Okounkov bodies, X-methods from MMP, and generic vanishing theory. We will report some progress on this subject based on the …
Speaker Feng Shao IBS, Center for Complex Geometry Let 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 …
Speaker Jie Liu Institute of Mathematics, AMSS, CAS It 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 …
Speaker Jihun Yum IBS, Center for Complex Geometry The Bergman kernel BX, which is by the definition the reproducing kernel of the space of L2 holomorphic n-forms on a n-dimensional complex manifold X, is one of the important objects in complex geometry. In this talk, we observe the asymptotics of the Bergman kernels, …
Speaker Giancarlo Urzúa Pontificia Universidad Catolica de Chile We defined wormholes in https://arxiv.org/abs/2102.02177 (joint with Nicolás Vilches). Conjecturally it is a way to non-continuous travel in the KSBA compactification of the moduli space of surfaces of general type. It depends on a particular MMP. In that paper, we verified the conjecture in several …
Speaker Kyoung-Seog Lee University of Miami Cox ring is an important tool in modern algebraic geometry and several other branches of mathematics. In the first part of this talk, I will briefly review basic theory of Cox ring and explain how it connects birational geometry and geometric invariant theory. Then I will discuss …
Speaker Sai-Kee Yeung Purdue University We 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.
List of Seminars On the Singular Loci of Higher Secants of Veronese Varieties Kangjin Han (DGIST) 14:00-14:50, online Manin’s Conjecture for a Log Del Pezzo Surface of Index 2 DongSeon Hwang (Ajou Univ.) 15:20-16:10, IBS B266 Ulrich Bundles on Cubic Fourfolds Yeongrak Kim (Pusan National Univ.) 16:30-17:20, IBS B266
Speaker Kangjin Han DGIST (This is a part of Algebraic Geometry Day at CCG in IBS.) For a projective variety X in PN, the k-secant variety σk(X) is defined to be the closure of the union of k-planes in PN spanned by k-points of X. In this talk, we consider singular loci of higher …
Speaker DongSeon Hwang Ajou Univ. (This is a part of Algebraic Geometry Day at CCG in IBS.) Manin’s conjecture predicts the asymptotic behavior on the number of rational points of bounded anticanonical height on Fano varieties. In this talk, I will explain how the geometry governs the arithmetic in the case of a …
Speaker Yeongrak Kim Pusan National Univ. (This is a part of Algebraic Geometry Day at CCG in IBS.) Ulrich bundles are geometric objects corresponding to maximally generated maximal Cohen-Macaulay modules, whose existence has several interesting applications in commutative algebra, homological algebra, and linear algebra. After a pioneering work of Beauville and Eisenbud-Schreyer, existence …
Speaker Olivier Martin Stony Brook Univ. I will discuss recent work in collaboration with R. Lazarsfeld which explores the following question: Given varieties X and Y of the same dimension how far are they from being birational? I will define various "measures of association" which quantify the failure of X and Y to …