Kristin DeVleming : K-moduli of curves on a quadric surface

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

At

Feb. 24, 2020, 4 p.m.

In

427 SEO

Abstract

I will discuss compactifications of the moduli space of (d,d) curves on P1xP1, focusing in particular on the case d = 4. We regard such a curve as a log Fano pair (P1xP1, aC), where a is a rational number, and study the compactifications coming from K stability and establish a wall crossing framework as a varies. In the case d = 4, Laza and O'Grady show that one can interpolate between the GIT moduli space of (4,4) curves and a Baily-Borel compactification of degree 4 K3 surfaces with a series of explicit VGIT wall crossings. We show that these VGIT walls coincide exactly with the K moduli walls described above. This is joint work with Kenneth Ascher and Yuchen Liu.