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Classification of genus 3 curves in special strata of the moduli space

Martine Girard·David R. Kohel
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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 $\Me_3$ of plane quartics which have at least seven hyperflexes, and obtain an computational characterization of curves in these strata.

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Martine Girard, David R. Kohel. 2006-03-23. Classification of genus 3 curves in special strata of the moduli space. https://arxiv.org/abs/math/0603555

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