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Covers of degree four and the rationality of the moduli space of curves of genus five with a vanishing theta-null
Published online by Cambridge University Press: 01 September 1998
Abstract
Let [Mfr ]g be the moduli space of smooth curves C of genus g[ges ]4 over the complex field [Copf ] and, as in [4], denote by [Mfr ](n)g⊂[Mfr ]g the locus of points representing curves having n vanishing theta-null, i.e. n points of order two in Sing (Θ).
I. V. Dolgachev proved the rationality of [Mfr ](1)4 (see [4, p. 13]) and of [Mfr ](2)5 (see [4, p. 11]). The aim of this paper is to prove the
Theorem. [Mfr ](1)tis rational.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 124 , Issue 2 , September 1998 , pp. 265 - 274
- Copyright
- Cambridge Philosophical Society 1998
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