Kenny Ascher : Wall crossings for K-moduli spaces

Posted by Izzet Coskun , part of the Algebraic Geometry Seminar.

At

Feb. 10, 2020, 4 p.m.

In

427 SEO

Abstract

K-stability has become a central tool in the study of compact moduli of Fano varieties. In this talk I will discuss K-stability compactifications of the moduli space of log Fano pairs (P2, aC), where C is a plane curve of degree at least 4 and a is a rational number. We establish a wall-crossing framework to study the behavior of these moduli spaces as the weight a varies. We show that when a is small, the K-moduli compactification is isomorphic to the GIT moduli space, and that the first wall crossing is a weighted blowup of Kirwan type. We describe all wall-crossings for degree 4, 5 and 6 and relate the final K-moduli spaces to Hacking's moduli space and some compact moduli of K3 surfaces. This is joint work with K. DeVleming and Y. Liu.