Ziquan Zhuang : Properness of the K-moduli space

Posted by Kevin Tucker , part of the Algebraic Geometry Seminar.

At

Nov. 15, 2021, 3 p.m.

In

Zoom

Abstract

K-stability is an algebraic condition that characterizes the existence of K\"ahler-Einstein metrics on Fano varieties. Recently there has been a lot of work on the construction of the K-moduli space, i.e. a good moduli space parametrizing K-polystable Fano varieties. Motivated by results in differential geometry, it is conjectured that this K-moduli space is proper and projective. In this talk, I'll discuss some recent progress in birational geometry that leads to a full solution of this conjecture. Based on joint work with Yuchen Liu and Chenyang Xu.