Compact moduli of K3 surfaces with a nonsymplectic automorphism

TL;DR

This paper develops a new compactification method for moduli spaces of K3 surfaces with nonsymplectic automorphisms, using stable pairs and proving its semitoroidal structure, advancing understanding of their geometric properties.

Contribution

It introduces a modular compactification for these moduli spaces via stable slc pairs, under specific fixed locus conditions, and demonstrates its semitoroidal nature.

Findings

Constructed a modular compactification for K3 moduli spaces

Proved the compactification is semitoroidal

Applicable under conditions on fixed loci of automorphisms

Abstract

We construct a modular compactification via stable slc pairs for the moduli spaces of K3 surfaces with a nonsymplectic group of automorphisms under the assumption that some combination of the fixed loci of automorphisms defines an effective big divisor, and prove that it is semitoroidal.