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

2024/12/15 by Alexeev, Valery, Deopurkar, Anand, Han, Changho
#14D22 #14J28 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2412.11256

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 ≥2. 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.

Related

• KSBA compactification of the moduli space of K3 surfaces with purely non-symplectic automorphism of order four
• Compact moduli of K3 surfaces with a nonsymplectic automorphism
• Compactifications of moduli spaces of K3 surfaces with a nonsymplectic involution
• Automorphism groups in a family of K3 surfaces
• Non-symplectic automorphisms of order 3 on K3 surfaces