A simple criterion for the uniruledness of an orthogonal modular variety

2025/03/20 by Ignacio Barros, Barros, Ignacio
Engineering · #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2503.16201

openalex publication_date 2025/03/20 · openalex created_date 2025/10/17 · openalex updated_date 2026/07/28

Abstract

We exhibit a simple uniruledness criterion for general orthogonal modular varieties in terms of invariants of the corresponding lattice. As an application, we obtain the uniruledness of almost all Nikulin--Vinberg moduli spaces parameterizing projective K3 surfaces of Picard number at least 3 and fixed finite automorphism group.

Related

• Uniruledness of orthogonal modular varieties
• Hirzebruch-Mumford proportionality and locally symmetric varieties of orthogonal type
• The Picard group of the Baily--Borel compactification of the moduli space of quasi-polarized K3 surfaces and generalizations
• Unirationality of moduli spaces of special cubic fourfolds and K3 surfaces
• Normal Forms, K3 Surface Moduli, and Modular Parametrizations