Moduli of plane quartics, Gopel invariants and Borcherds products

2009/06/15 by Shigeyuki Kondō, Shigeyuki Kondo, Kondo, Shigeyuki · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #math.AG

paper · pdf · doi:10.48550/arxiv.0906.2598

arxiv created 2009/06/15 · openalex publication_date 2009/06/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is known that the moduli space of plane quartic curves is birational to an arithmetic quotient of a 6-dimensional complex ball. In this paper, we shall show that there exists a 15-dimensional space of meromorphic automorphic forms on the complex ball which gives a birational embedding of the moduli space of plane quartics with level 2 structure into 14-dimensional projective space. This map coincides with the one given by Coble by using Gopel invariants.

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• Moduli spaces of sextic curves with simple singularities and their compactifications

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