English

Compactifications of moduli spaces of K3 surfaces with a nonsymplectic involution

Algebraic Geometry 2023-05-15 v2 Mathematical Physics math.MP

Abstract

There are 7575 moduli spaces FSF_S of K3 surfaces with a nonsymplectic involution. We give detailed descriptions of Kulikov models for one-parameter degenerations in FSF_S. In the 5050 cases where the fixed locus of the involution has a component CgC_g of genus g2g\ge2, we identify normalizations of the KSBA compactifications of FSF_S via stable pairs (X,ϵCg)(X,\epsilon C_g), with explicit semitoroidal compactifications of FSF_S.

Keywords

Cite

@article{arxiv.2208.10383,
  title  = {Compactifications of moduli spaces of K3 surfaces with a nonsymplectic involution},
  author = {Valery Alexeev and Philip Engel},
  journal= {arXiv preprint arXiv:2208.10383},
  year   = {2023}
}

Comments

v2: More examples added and the references updated. 18 figures, 2 tables