Reduction of Plane Quartics and Dixmier-Ohno invariants

Authors:
  • RBRaymond van Bommel
    Raymond van Bommel
  • JDJordan Docking
    Jordan Docking
  • RLReynald Lercier
    Reynald Lercier
  • EGElisa Lorenzo García
    Elisa Lorenzo García
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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.