Reduction Types of Genus-3 Curves in a Special Stratum of their Moduli Space

Irene Bouw, Nirvana Coppola, Pınar Kılıçer, Sabrina Kunzweiler, Elisa Lorenzo García, Anna Somoza*

*Corresponding author for this work

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We study a 3-dimensional stratum ℳ3 , V of the moduli space ℳ3 of curves of genus 3 parameterizing curves Y that admit a certain action of V = C2 × C2. We determine the possible types of the stable reduction of these curves to characteristic different from 2. We define invariants for ℳ3 , V and characterize the occurrence of each of the reduction types in terms of them. We also calculate the j-invariant (respectively the Igusa invariants) of the irreducible components of positive genus of the stable reduction Y in terms of the invariants.

Original languageEnglish
Title of host publicationWomen in Numbers Europe III
Subtitle of host publicationResearch Directions in Number Theory
EditorsAlina Carmen Cojocaru, Sorina Ionica, Elisa Lorenzo García
Number of pages48
ISBN (Electronic)978-3-030-77700-5
ISBN (Print)978-3-030-77699-2
Publication statusPublished - 2021

Publication series

NameAssociation for Women in Mathematics Series
ISSN (Print)2364-5733
ISSN (Electronic)2364-5741


  • Dixmier–Ohno invariants
  • Plane quartic curves
  • Stable reduction

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