Moduli of K3 surfaces of degree 2 with four rational double points of type D₄

2024/03/07 by Ueda, Kazushi
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2403.04177

Abstract

We show that the Satake-Baily-Borel compactification of the moduli space of lattice polarized K3 surfaces parametrizing K3 surfaces of degree 2 with four rational double points of type D₄ is the projective 3-space. We also show that the corresponding graded ring of automorphic forms is generated by four elements of weight 2 and one element of weight 11 with one relation of weight 22.

Related

• Compact moduli of K3 surfaces
• KSBA compactification of the moduli space of K3 surfaces with purely non-symplectic automorphism of order four
• Moduli space of quasi-polarized K3 surfaces of degree 6 and 8
• On K3 surfaces of Picard rank 14
• On lattice-polarized K3 surfaces