Computing degenerations of K3 surfaces via Tschirnhausen bundles
ABSTRACT
A K3 surface with a nonsymplectic automorphism of order 3 is a triple cover of a rational surface. The moduli space of such K3 surfaces admits several compactifications — Baily-Borel, toroidal, and KSBA — whose boundary strata parameterizes datas coming from limiting mixed Hodge structures. But what do the boundary surfaces actually look like? I will explain how to explicitly construct degenerations of those K3 surfaces via the Tschirnhausen bundle of triple covers of nodal rational curves. This talk is based on several joint works with Valery Alexeev, Anand Deopurkar, and Philip Engel.
