School of Mathematical Sciences

K-moduli space of del Pezzo surface pairs

Thursday 1st June 2023 (10:00-11:00)
Event Convenor Contact:
Speaker's Name: Fei Si
Speaker's Affiliation: BICMR
Speaker's Research Theme(s): Algebraic Geometry seminar,
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 ~ −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.

Venue: Teams
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School of Mathematical Sciences

The University of Nottingham
University Park
Nottingham, NG7 2RD

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