복소기하학연구단
Speaker Chuyu Zhou Yonsei University We will present various criterion for K-stability for Fano varieties, including viewpoints from test configurations, valuations, and filtrations.
Speaker Chuyu Zhou Yonsei University We will present the construction of moduli space of Fano varieties with K-stability, including defining the moduli functor, showing various good properties of the functor, and introducing Alper-Halpern Leistner-Heinloth criterion for the existence of good moduli space.
Speaker Chuyu Zhou Yonsei University We will introduce a novel characteristic of K-stability, i.e. wall crossing phenomenon, and present a comparison between K-stability and GIT-stability. Time permitting, we will survey some open problems.
Speaker Benjamin Bakker Univ. Illinois Chicago Compact hyperkahler manifolds X are higher-dimensional generalizations of K3 surfaces; their geometry is tightly constrained by the existence of a holomorphic symplectic form. For example, a result of Matsushita says the only nontrivial fibration structures f:X→B they admit are fibrations by Lagrangian tori. In this talk, I …
Speaker Benjamin Bakker Univ. Illinois Chicago Matsushita conjectured that for any Lagrangian fibration f:X→B of a compact hyperkahler manifold X, the fibers deform either maximally or trivially in moduli. In this talk I'll explain how to prove this conjecture via Hodge theory. I will also discuss some other features of the topology of …
Speaker Shigeyuki Kondo Nagoya University The Enriques surface was discovered, in 1894 by Federigo Enriques, as a counter-example of a rationality problem. First I would like to recall the moduli space and the automorphism groups of Enriques surfaces over the complex numbers. In the later half, I shall mention a recent progress in …
Speaker Shigeyuki Kondo Nagoya University The Enriques surface was discovered, in 1894 by Federigo Enriques, as a counter-example of a rationality problem. First I would like to recall the moduli space and the automorphism groups of Enriques surfaces over the complex numbers. In the later half, I shall mention a recent progress in …
Speaker Hsueh-Yung Lin National Taiwan University The motivic invariant c(f) of a birational automorphism f : X - → X measures the difference between the birational types of the exceptional divisors of f and those of the inverse f-1. In general c(f) is nonzero: this is the case when f is some Cremona …
Speaker Ching-Jui Lai National Cheung Kung University The set of canonical Fano threefolds form a bounded family by results of Kawamata, Mori-Miyaoka-Kollar-Tagaki, and in a much more general setting by Birkar. In particular, the anticaonical volume -KX3 is bounded. An optimal lower bound is 1/330 by the work of Chen-Chen. In this talk, …
Speakers Lorenzo Barban (IBS-CCG) Jungkai Chen (National Taiwan University) Toshiyuki Katsura (University of Tokyo) Shigeyuki Kondo (Nagoya University) Ching-Jui Lai (National Cheung Kung University) Donggun Lee (IBS-CCG) Hsueh-Yung Lin (National Taiwan University) Shigeru Mukai (Kyoto University) Keiji Oguiso (University of Tokyo) Abstracts PDF file Schedule May 14 (Tuesday) 14:00~14:20 Registration 14:20~15:20 Oguiso 15:40~16:40 Lai 17:00~18:00 …
Speaker Jungkai Chen National Taiwan University The minimal model program works pretty well in dimension three. However, the explicit classification of divisorial contractions to points was completed quite recently thanks to the work of Kawamata, Hayakawa, Kawakita and more. In this talk, we are going to describe threefold divisorial contractions to curves. We …
Speaker Shigeru Mukai RIMS, Kyoto University I will discuss the moduli space of abelian surfaces with bi-level structure of type (1, d) for d = 2, 3, 4, 5. Part 1: Their Satake compactification is the projective 3-space P3 for d = 2, 3, 4. Part 2: It is a small contraction of …