복소기하학연구단
Speaker Jinhyung Park Sogang University There 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 …
Speaker Sung Rak Choi Yonsei University We 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 …
Speaker Changho Han University of Georgia Observe that any construction of "meaningful" compactification of moduli spaces of objects involve enlarging the class of objects in consideration. For example, Deligne and Mumford introduced the notion of stable curves in order to compactify the moduli of smooth curves of genus g, and Satake used the …
Speaker Yoon-Joo Kim Stony Brook University A compact hyper-Kähler manifold is a higher dimensional generalization of a K3 surface. An elliptic fibration of a K3 surface correspondingly generalizes to the so-called Lagrangian fibration of a compact hyper-Kähler manifold. It is known that an elliptic fibration of a K3 surface is always "self-dual" in …
Speaker Yuchen Liu Northwestern University We show that K-moduli spaces of (P3, cS) where S is a quartic surface interpolates between the GIT moduli space and the Baily-Borel compactification as c varies in (0,1). We completely describe the wall crossings of these K-moduli spaces. As a consequence, we verify Laza-O’Grady's prediction on the …
Speaker Yewon Jeong IBS, Center for Complex Geometry Given 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 …
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 …