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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

G. CASNATI  and
A. DEL CENTINA
G. CASNATI
Affiliation:
Dipartimento di Matematica Pura ed Applicata, Università degli Studi di Padova, via Belzoni 7, I-35131 Padova, Italy; e-mail: [email protected]
A. DEL CENTINA
Affiliation:
Dipartimento di Matematica, Università degli Studi di Ferrara, via Machiavelli 35, 44100 Ferrara, Italy; e-mail: [email protected]
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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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