Reduction of plane quartics and Dixmier–Ohno invariants
Open Access
- 24 February 2025
- journal article
- research article
- Published by Springer Nature in Research in Number Theory
- Vol. 11 (1) , 1-25
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.Keywords
All Related Versions
This publication has 21 references indexed in Scilit:
- Reduction Types of Genus-3 Curves in a Special Stratum of their Moduli Space2021
- Explicit computations of invariants of plane quartic curvesJournal of Symbolic Computation, 2015
- Hyperelliptic curves and their invariants: Geometric, arithmetic and algorithmic aspectsJournal of Algebra, 2012
- The moduli spaces of hyperelliptic curves and binary formsMathematische Zeitschrift, 2002
- The Magma Algebra System I: The User LanguageJournal of Symbolic Computation, 1997
- Courbes stables de genre 2 et leur sch ma de modulesMathematische Annalen, 1993
- Construction de courbes de genre 2 à partir de leurs modules1991
- On the projective invariants of quartic plane curvesAdvances in Mathematics, 1987
- The irreducibility of the space of curves of given genusPublications mathématiques de l'IHÉS, 1969
- Geometric Invariant Theory1965