복소기하학연구단
Speakers Woohyeok Jo (Seoul National U.) Jongil Park (Seoul National U.) Kyungbae Park (Kangwon National U.) Abstracts PDF file Schedule August 7 (Fri) 10:30-12:00 Jongil Park 14:00-15:30 Woohyeok Jo August 8 (Sat) 10:30-12:00 Kyungbae Park 14:00-16:00 Jongil Park & Kyungbae Park Organizers JongHae Keum (KIAS) DongSeon Hwang (IBS-CCG) Venue 8101, KIAS, Seoul, Korea
Speaker Guolei Zhong East China Normal University Positivity properties of tangent sheaves are known to impose strong restrictions on the global geometry of projective varieties and, more generally, compact Kähler varieties. In this talk, after briefly reviewing the background, we will present several structural results for compact Kähler varieties with pseudo-effective tangent sheaf. …
Speaker David Sykes IBS-CCG This talk will introduce a natural construction for encoding codimension 1 pseudo-product structures into filtered manifolds amenable to analysis by Tanaka prolongation techniques, and its application to local geometry of CR hypersurfaces. Classically, Tanaka prolongation has only been applicable to maximally nondegenerate pseudo-product structures, while our new techniques require …
Speaker Sönke Rollenske Marburg University In the study of (relatively minimal) elliptic surfaces $f\colon S \to C$ with a section, the Weierstrass model plays an important role. We discuss two different models for elliptic surfaces with a bisection (or more generally an $f$-nef divisor which has degree two on the fibres): a birational …
Speaker Sönke Rollenske Marburg University Compact quotients of non-abelian complex nilpotent Lie groups are non-Kähler manifolds with trivial canonical bundle, the most prominent example being the Iwasawa manifold. We give a precise characterisation of the (rare) cases where deformations of such manifolds are unobstructed in terms of so-called verbal ideals in free nilpotent …
Speaker Yewon Luke Cho Gyeongsang National U A characterization of noncompact ball quotients by Munteanu (2009) implies that only complete Kähler-Einstein metrics on certain noncompact ball quotients maximize the bottom of the spectrum among complete Kähler metrics with Ricci curvature bounded below by -1. In this talk, I will report my recent observation, …
Speaker Xian Wu Yonsei University We begin with an overview of the framework of KSBA (Kollár—Shepherd-Barron—Alexeev) moduli spaces and stable degenerations, emphasizing some phenomena that distinguish the higher-dimensional cases from the Deligne–Mumford moduli of stable curves. We then survey several existing explicit constructions of KSBA compactifications. As a detailed example, we discuss the …
Speaker In-Kyun Kim HCMC KIAS A variety $X$ is called cylindrical if it contains a Zariski-open subset isomorphic to $Z \times \mathbb A^1$ for some affine variety $Z$. If such an open subset is the complement of the support of an effective $\mathbb{Q}$-divisor $D$ satisfying $D \sim_{\mathbb Q} -K_X$, then it is called …
Speaker Michael Albanese Adelaide University A nearly Kähler six-manifold admits a compatible SU(3)-structure. Verbitsky utilised this SU(3)-structure to obtain a generalisation of the Kähler identities, which he used to prove a Hodge decomposition analogous to the Kähler case. We extend these identities and the Hodge decomposition to nearly Kähler manifolds in arbitrary dimensions. …
Speaker Qifeng Li Shandong University The fundamental form is a basic object for manifolds and varieties. In this talk, we will give a bound on the dimension of the linear automorphism group of a projective variety $Z \subset \mathbb{P} V$ in terms of its fundamental forms at a general point. Moreover, we will …
Speaker Yingqi Liu IBS CCG Hwang and Li introduced cone structures with characteristic conic connections, partially generalizing VMRT structures on uniruled projective manifolds. For isotrivial cone structures with fiber Z, they established a projective-geometric criterion on Z ensuring the existence of torsion-free connections on the associated G-structures. In this talk, I will describe …
Speaker for lecture series Eunjeong Lee (Chungbuk National University) Speakers for research talk Byung Hee An (Kyungpook National University) Myungho Kim (Kyung Hee University) Abstracts PDF file Schedule October 22 (Thursday) 10:30-12:00 Eunjeong Lee, Lecture 1 14:00-15:30 Eunjeong Lee, Lecture 2 16:00-17:00 Myungho Kim 18:00- Banquet October 23 (Friday) 10:30-12:00 Eunjeong Lee, Lecture 3 …