Compactifications of moduli spaces of K3 surfaces with a nonsymplectic involution

TL;DR

This paper studies the compactifications of moduli spaces of K3 surfaces with nonsymplectic involutions, providing detailed models for degenerations and explicit descriptions of their compactifications.

Contribution

It offers a comprehensive analysis of Kulikov models and identifies explicit semitoroidal compactifications for these moduli spaces.

Findings

Descriptions of Kulikov models for degenerations in all cases.

Identification of KSBA compactifications with explicit semitoroidal models.

Detailed classification of fixed locus components and their impact on compactifications.

Abstract

There are $75$ moduli spaces $F_S$ of K3 surfaces with a nonsymplectic involution. We give detailed descriptions of Kulikov models for one-parameter degenerations in $F_S$. In the $50$ cases where the fixed locus of the involution has a component $C_g$ of genus $g\ge2$, we identify normalizations of the KSBA compactifications of $F_S$ via stable pairs $(X,\epsilon C_g)$, with explicit semitoroidal compactifications of $F_S$.