On the number of moduli of plane sextics with six cusps

Details On the number of moduli of plane sextics with six cusps On the number of moduli of plane sextics with six cusps

2007-04-04

arxiv.org/abs/0704.0622v1

Mathematics

Algebraic Geometry

9 pagine

Scientific paper

Let S be the variety of irreducible sextics with six cusps as singularities. Let W be one of irreducible components of W. Denoting by M_4 the space of moduli of smooth curves of genus 4, the moduli map of W is the rational map from W to M_4 sending the general point of W, corresponding to a plane curve D, to the point of M_4 parametrizing the normalization curve of D. The number of moduli of W is, by definition the dimension of the image of W with respect to the moduli map. We know that this number is at most equal to seven. In this paper we prove that both irreducible components of S have number of moduli exactly equal to seven.

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