On the moduli space of smooth plane quartic curves with a sextactic point

Abstract

Let Mg be the moduli space of smooth algebraic curves of genus g over C: In this paper, we prove that the set Sr M 3 of moduli points of smooth plane quartic curves (nonhyperelliptic curves of genus 3) having at least one sextactic point of sextact multiplicity r; where r 2 f1;2;3g; is an irreducible, closed and rational subvariety of codimensional r 1 of M3 H 3 (where H3 M 3 is the hyperelliptic locus ).