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Compactifications of moduli spaces of K3 surfaces with a higher-order nonsymplectic automorphism

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arxiv 2412.11256 v2 pith:IFOTL57F submitted 2024-12-15 math.AG

Valery Alexeev , Anand Deopurkar , Changho Han This is my paper · ORCID
classification math.AG
keywords automorphismcompactificationsksbamodulinonsymplecticorderspacessurfaces
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abstract

We describe Baily-Borel, toroidal, and geometric -- using the KSBA stable pairs -- compactifications of some moduli spaces of K3 surfaces with a nonsymplectic automorphism of order $3$ and $4$ for which the fixed locus of the automorphism contains a curve of genus $\ge2$. For order $3$, we treat all the maximal-dimensional such families. We show that the toroidal and the KSBA compactifications in these cases admit simple descriptions in terms of certain $ADE$ root lattices.

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  1. 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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