具有奇特征的三格曲线的模空间是有理的

Indagationes Mathematicae (Proceedings) Pub Date : 1987-03-30 DOI:10.1016/S1385-7258(87)80001-X

Fabio Bardelli

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引用次数: 2

摘要

本文利用Sylvester给出的广义三次曲面方程的“正规形式”，证明了%plane1D;4B0;={具有S个光滑三次曲面的对(S,P)的模空间，S}上的点P是有理的。然后证明了%plane1D;510; 30 ={3属曲线和一个奇特征曲线的模空间}与%plane1D;4B0;如此理性。

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The moduli space of curves of genus three together with an odd theta-characteristic is rational

In this note we use a “normal form”, due to Sylvester, for the equation of a generic cubic surface in ℙ³(ℂ) to prove that %plane1D;4B0;= {moduli space of pairs (S,P) with S smooth cubic surface, P a point on S} is rational. We then prove that %plane1D;510;₃^oth = {moduli space of curves of genus three together with one odd theta-characteristic} is birational to %plane1D;4B0; and so rational.

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Indagationes Mathematicae (Proceedings)

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