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

Alwaleed Kamel, M. Farahat
2013 Applied Mathematics & Information Sciences  
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 ∈ {1, 2, 3}, is an irreducible, closed and rational subvariety of codimensional r − 1 of M3 − H3 (where H3 ⊂ M3 is the hyperelliptic locus ).
doi:10.12785/amis/070211 fatcat:w5tgyjzd7fffrgyjlv5ajelmji