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<p>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.</p>

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Reduction of plane quartics and Dixmier–Ohno invariants

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年2月24日

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  • Raymond van Bommel,
  • Jordan Docking,
  • Reynald Lercier,
  • Elisa Lorenzo García

摘要

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.