Reduction of Plane Quartics and Dixmier-Ohno invariants

2024/01/25 by van Bommel, Raymond, Docking, Jordan, Lercier, Reynald +1 · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2401.13902

Abstract

We characterise, in terms of Dixmier-Ohno invariants, the types of singularities that a plane quartic curve can have. We then use these results to obtain new criteria for determining the stable reduction types of non-hyperelliptic curves of genus 3.

Cited by

• Automorphism groups and linearizability of rational Fano conic bundle threefolds

Related

• Stable models of plane quartics with hyperelliptic reduction
• Classification of genus 3 curves in special strata of the moduli space
• Semistable Reduction of Plane Quartics
• Reduction of Plane Quartics and Cayley Octads
• Semistable reduction of smooth quartics