Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-26T16:37:43.674Z Has data issue: false hasContentIssue false
  • English
  • Français

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]
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)