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Compactifications of moduli spaces of K3 surfaces with a nonsymplectic involution

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arxiv 2208.10383 v2 pith:MGFQGTFC submitted 2022-08-22 math.AG math-phmath.MP

Valery Alexeev , Philip Engel This is my paper · ORCID
classification math.AGmath-phmath.MP
keywords compactificationsinvolutionmodulinonsymplecticspacessurfacescasescomponent
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Polync varieties and multiparameter Kulikov models

    math.AG 2026-01 conditional novelty 7.0 of 10

    Polync varieties generalize normal-crossing degenerations; the paper proves d-semistable K-trivial polync varieties are smoothable and constructs multiparameter Kulikov models with explicit examples.

  2. Normal stable degenerations of Noether-Horikawa surfaces

    math.AG 2025-07 conditional novelty 7.0 of 10

    Every Q-Gorenstein smoothable normal stable Horikawa surface falls into one of seven explicit families, and its global smoothability is controlled by a single local condition at its elliptic double cone singularities.

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