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

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Algorithmic Number Theory (ANTS 2006)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 4076))

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Abstract

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.

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Author information

Authors and Affiliations

  1. School of Mathematics and Statistics, The University of Sydney,  

    Martine Girard & David R. Kohel

Authors
  1. Martine Girard
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  2. David R. Kohel
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Editor information

Editors and Affiliations

  1. Technische Universität Berlin, Germany

    Florian Hess

  2. Institut für Mathematik, MA 8–1, Technische Universität Berlin, Straße des 17. Juni 136, 10623, Berlin, Germany

    Sebastian Pauli

  3. Institut für Mathematik, Technische Universität Berlin, Fakultät II, MA 8-1, Strasse des 17. Juni 136, 10623, Berlin, Germany

    Michael Pohst

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Girard, M., Kohel, D.R. (2006). Classification of Genus 3 Curves in Special Strata of the Moduli Space. In: Hess, F., Pauli, S., Pohst, M. (eds) Algorithmic Number Theory. ANTS 2006. Lecture Notes in Computer Science, vol 4076. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11792086_25

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  • DOI: https://doi.org/10.1007/11792086_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-36075-9

  • Online ISBN: 978-3-540-36076-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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