Birational Geometry of Moduli Spaces of Del Pezzo Surface Pairs
Dr. Fei Si
2023-10-17 10:00-11:30
MCM410
Speaker: Dr. Fei Si (Peking Univ)Time: 10:00-11:30 October 17, 2023 (Tuesday)
Place: MCM410
Title: Birational Geometry of Moduli Spaces of Del Pezzo Surface Pairs
Abstract: A K3 surfaces with an anti-symplectic involution is equivalent to a del pezzo surface pair (X, C) where X is a del pezzo surface and C is a curve on X so that C~-2KX. Their moduli spaces have many compactifications cations from different perspectives like GIT, Hodge theory and K-stability theory. It is natural to ask what is the precise relations of these compatifications? In this talk, I will provide a solution by viewing these compatifications as log canonical models of Baily-Borel compatification for degree 8 pairs. It is now known as Hassett-Keel-Looijenga program as initiated by Laza-O'Grady in the case of quartic K3 surfaces. Via this viewpoint, we can also obtain the K-moduli walls from an arithmetic stratification. This is based on joint work with Long Pan and Haoyu Wu.
