복소기하학연구단
Speaker In-Kyun Kim KIAS In algebraic geometry, constructing moduli spaces that parametrize families of algebraic varieties with certain properties is an important problem. In the case of Fano varieties, the construction of moduli spaces is a challenging problem. K-stability provides a criterion for selecting nice representatives within the moduli space, which helps create …
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 Sung Rak Choi Yonsei University In this talk, we define and study a triple called a potential triple which consists of a pair (X, Δ) and a polarizing pseudoeffective divisor D. To such a triple, we define a so-called potential multiplier ideal sheaf which gives a simultaneous generalization of the multiplier ideal …
Speaker Eric Sommers University of Massachusetts Among the nilpotent orbits in a simple Lie algebra are the special nilpotent orbits, which play an important role in representation theory. Some of the geometry of the closure of a nilpotent orbit can be understood by taking a transverse slice to a smaller orbit in the …
Speaker Cheol Hyun Cho Seoul National University The variation operator in singularity theory maps relative homology cycles to compact cycles in the Milnor fiber using the monodromy. We construct its symplectic analogue for an isolated singularity. We define a new Floer cohomology, called monodromy Lagrangian Floer cohomology, which provides categorifications of the standard …
Speaker Sheng Meng East China Normal University Let X be a normal projective variety over C. Let f be a surjective endomorphism of X. In this talk, I will try to explain our current program on the classification and the building blocks of (f, X), involving two main tools: equivariant minimal model program …
Speaker Chuyu Zhou Yonsei University In this lecture, I will recall some basic knowledge on K-stability and some background on wall crossing in proportional setting. Then we plan to conduct a comparison between proportional case and non-proportional case. Under the comparison, we will define several domains associated to a family of couples and …
Speaker Chuyu Zhou Yonsei University In this lecture, we will talk about two properties of K-semistable domains in non-proportional setting. One is the finiteness criterion, which states that the number of domains is finite for a family of couples. The other is about the shape of each domain, which states that they are …