On the number of moduli of plane sextics with six cusps
Abstract
Let S be the variety of irreducible sextics with six cusps as singularities. Let W be one of irreducible components of W. Denoting by M4 the space of moduli of smooth curves of genus 4, the moduli map of W is the rational map from W to M4 sending the general point of W, corresponding to a plane curve D, to the point of M4 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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