Compactifications of moduli spaces of K3 surfaces with a nonsymplectic involution

Valery Alexeev; Philip Engel

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arXiv · 2208.10383

Compactifications of moduli spaces of K3 surfaces with a nonsymplectic involution

Valery Alexeev·Philip Engel

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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 $F_S$.

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BibTeX RIS

Valery Alexeev, Philip Engel. 2022-08-22. Compactifications of moduli spaces of K3 surfaces with a nonsymplectic involution. https://arxiv.org/abs/2208.10383

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