On the number of moduli of plane sextics with six cusps期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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On the number of moduli of plane sextics with six cusps

Authors:	Concettina Galati

Institution:	(1) Dipartimento di Matematica, Università della Calabria, 87036 Arcavacata di Rende (CS), Italy

Abstract:	Let ${\Sigma_{6,0}^6}$ be the variety of irreducible sextics with six cusps as singularities. Let ${\Sigma \subset \Sigma_{6,0}^6}$ be one of irreducible components of ${\Sigma_{6,0}^6}$ . Denoting by ${\mathcal{M}_{4}}$ the space of moduli of smooth curves of genus 4, we consider the rational map ${\Pi : \Sigma \dashrightarrow \mathcal{M}_{4}}$ sending the general point Γ] of Σ, corresponding to a plane curve ${\Gamma \subset \mathbb{P}^{2}}$ , to the point of ${\mathcal{M}_{4}}$ parametrizing the normalization curve of Γ. The number of moduli of Σ is, by definition the dimension of Π(Σ). We know that ${{\rm dim}(\Pi(\Sigma)) \leq {\rm dim}(\mathcal{M}_{4}) + \rho(2, 4, 6) - 6 = 7}$ , where ρ(2, 4, 6) is the Brill–Noether number of linear series of dimension 2 and degree 6 on a curve of genus 4. We prove that both irreducible components of ${\Sigma_{6,0}^6}$ have number of moduli equal to seven.

Keywords:	Number of moduli Sextics with six cusps Plane curves Zariski pairs
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