K-moduli space of del Pezzo surface pairs

Date(s): Thursday 1st June 2023 (10:00-11:00)
Contact: Event Convenor Contact: A.M.Kasprzyk@nottingham.ac.uk
Description: Speaker's Name: Fei Si
Speaker's Affiliation: BICMR
Speaker's Research Theme(s): Algebraic Geometry seminar,
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 ~ −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
Online Conference Link: https://teams.microsoft.com/l/meetup-join/19%3abc0bccd250d74459ac05c0b3e0ff9b76%40thread.tacv2/1682514080426?context=%7b%22Tid%22%3a%2267bda7ee-fd80-41ef-ac91-358418290a1e%22%2c%22Oid%22%3a%222dbd114f-1c6d-4e8b-aab9-fadd00bd8602%22%7d

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