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

Valery Alexeev; Anand Deopurkar; Changho Han

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

Algebraic Geometry 2025-02-12 v2

Authors: Valery Alexeev , Anand Deopurkar , Changho Han

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.

Keywords

moduli spaces K3 surfaces nonsymplectic automorphism Baily-Borel compactification toroidal compactification

Cite

@article{arxiv.2412.11256,
  title  = {Compactifications of moduli spaces of K3 surfaces with a higher-order nonsymplectic automorphism},
  author = {Valery Alexeev and Anand Deopurkar and Changho Han},
  journal= {arXiv preprint arXiv:2412.11256},
  year   = {2025}
}

Comments

55 pages, 24 figures. v2: Updated references, and improved expositions by making extensive use of period domains of Type II Kulikov surfaces

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

Abstract

Keywords

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