Algebraic Geometry Seminar: "Compactifications of an interesting family of K3 surfaces from 8 points in P^1"

Speaker: Luca Schaffler, University of Massachusetts-Amherst

Abstract: In the study of higher dimensional algebraic varieties, moduli spaces play a central role, and studying different compactifications provides information about their birational geometry.
In this talk, we consider the moduli space of K3 surfaces with order 4 purely non-symplectic automorphism and a specific lattice polarization. Kondo constructed these surfaces from eight points in $\mathbb{P}^1$ as double covers of $\mathbb{P}^1\times\mathbb{P}^1$. Work of Deligne and Mostow implies that the GIT compactification of this moduli space is isomorphic to the Baily-Borel compactification. But these compactifications have weak geometric meaning.

We prove that Kirwan's partial desingularization of the GIT compactification has a modular interpretation in terms of KSBA stable pairs, and hence it carries very rich geometric meaning. We describe the
degenerations parametrized by the boundary and the singularities that occur. This is joint work with Han-Bom Moon.

Host: Matt Kerr