Compactifications of moduli spaces of K3 surfaces with a nonsymplectic involution

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 $g\ge 2$, we identify normalizations of the KSBA compactifications of $F_S$ via stable pairs $(X,\epsilon C_g)$, with explicit semitoroidal compactifications of $F_S$.

v2: More examples added and the references updated. 18 figures, 2 tables