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arXiv · 2412.11256

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

Valery Alexeev·Anand Deopurkar·Changho Han
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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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Valery Alexeev, Anand Deopurkar, Changho Han. 2024-12-15. Compactifications of moduli spaces of K3 surfaces with a higher-order nonsymplectic automorphism. https://arxiv.org/abs/2412.11256

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