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

Authors

Alwaleed Kamel, Freie Universitt Berlin, Fachbereich Mathematik und Informatik, Mathematisches Institut, Berlin, Germany
M. Farahat

Author Country (or Countries)

Germany

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⊆ M3 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 ).

Suggested Reviewers

N/A

Recommended Citation

Kamel, Alwaleed and Farahat, M. (2013) "On the moduli space of smooth plane quartic curves with a sextactic point," Applied Mathematics & Information Sciences: Vol. 07: Iss. 2, Article 10.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol07/iss2/10