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

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 M3 of plane quartics which have at least seven hyperflexes, and obtain an computational characterization of curves in these strata. © Springer-Verlag Berlin Heidelberg 2006.