Classification of genus 3 curves in special strata of the moduli space

2006/03/23 by Martine Girard, Girard, Martine, David Kohel +2
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Number Theory (math.NT) #math.AG #math.NT

paper · pdf · doi:10.48550/arxiv.math/0603555

arxiv created 2006/03/23 · openalex publication_date 2006/03/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe the invariants of plane quartic curves -- nonhyperelliptic genus 3 curves in their canonical model -- as determined by Dixmier and Ohno, with application to the classification of curves with given structure. In particular, we determine modular equations for the strata in the moduli space \Me₃ of plane quartics which have at least seven hyperflexes, and obtain an computational characterization of curves in these strata.

Related

• Non hyperelliptic curves of genus three over finite fields of characteristic two
• Reduction of Plane Quartics and Dixmier-Ohno invariants
• Heegner divisors in the moduli space of genus three curves
• Twists of non-hyperelliptic curves of genus 3
• On hyperelliptic curves of genus 3