K-moduli space of del Pezzo surface pairs

Abstract: A K3 surfaces with anti-symplectic involution can be identified with a pair $(X,C)$ consisting of a del Pezzo surface $X$ with a curve $C \sim −2K_X$. Their moduli space has many compactifications from various perspectives. In this talk, we will discuss the compactifications from $K$-moduli theoretic side and its relation to Baily-Borel compactification from Hodge theoretic side. In particular, we will give an explicit description of $K$-moduli space $P_c^K$ parametrizing $K$-polystable del Pezzo pairs $(X,cC)$ under the framework of wall-crossing for $K$-moduli space due to Ascher-DeVleming-Liu. Moreover, we will show the $K$-moduli space $P_c^K$ is isomorphic to certain log canonical model on Baily-Borel compactification of the moduli space of K3 surfaces with anti-symplectic involution. This can be viewed as another example of Hassett-Keel-Looijenga program proposed by Laza-O'Grady. This is based on joint work with Long Pan and Haoyu Wu.

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