Algebraic Geometry Seminar
Kristin DeVleming
University of California San Diego
K-moduli of curves on a quadric surface
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.
Monday February 24, 2020 at 4:00 PM in 427 SEO