K moduli of quartic K3 surfaces

Abstract: We will discuss a family of compactifications of moduli spaces of log Fano pairs coming from K-stability, and discuss an application to moduli of quartic K3 surfaces, with a focus on the locus of hyperelliptic K3s that arise as double covers of $\mathbb{P}^1\times\mathbb{P}^1$ branched over a $(4,4)$ curve. We will show that K-stability provides a natural way to interpolate between the GIT moduli space and the Baily-Borel compactification and will relate this interpolation to VGIT wall crossings. This is joint work with Kenny Ascher and Yuchen Liu.

algebraic geometrycombinatorics

Audience: researchers in the topic

Online Nottingham algebraic geometry seminar

Series comments: Online geometry seminar, typically held on Thursday. This seminar takes place online via Microsoft Teams on the Nottingham University "Algebraic Geometry" team.

For recordings of past talks, copies of the speaker's slides, or to be added to the Team, please visit the seminar homepage at: kasprzyk.work/seminars/ag.html