Classification of Genus 3 Curves in Special Strata of the Moduli Space

  • Martine Girard
  • David R. Kohel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4076)


We describe the invariants of plane quartic curves — nonhyperelliptic genus 3 curves in their canonical model — as determined by Dixmier and Ohno, with application to the classification of curves with given structure. In particular, we determine modular equations for the strata in the moduli space \({\mathcal M}_3\) of plane quartics which have at least seven hyperflexes, and obtain an computational characterization of curves in these strata.


Modulus Space Canonical Model Weierstrass Point Galois Cover Modular Equation 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Martine Girard
    • 1
  • David R. Kohel
    • 1
  1. 1.School of Mathematics and StatisticsThe University of Sydney 

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