On the number of moduli of plane sextics with six cusps

Concettina Galati

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arXiv · 0704.0622

On the number of moduli of plane sextics with six cusps

Concettina Galati

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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 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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BibTeX RIS

Concettina Galati. 2007-04-04. On the number of moduli of plane sextics with six cusps. https://arxiv.org/abs/0704.0622

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