Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

The Rationality of the Moduli Space of Bielliptic Curves of Genus Five

The Rationality of the Moduli Space of Bielliptic Curves of Genus Five THE RATIONALITY OF THE MODULI SPACE OF BIELLIPTIC CURVES OF GENUS FIVE G. CASNATI AND A. DEL CENTINA 0. Introduction and notation Let C be an irreducible, smooth, projective curve of genus g ^ 2, defined over the complex field C, and let yjl be the coarse moduli space of smooth curves of genus g. C is called bielliptic if it admits a degree 2 morphism n.C^E onto an elliptic curve E. We denote by 9CR£ c yjl the moduli space of bielliptic curves of genus g. The aim of this paper is to present a proof of the following. THEOREM 0.1. 9W£ is rational. For this we proceed as follows. If [CJeSK!? , then the canonical model C of C is the base locus of a net of quadric hypersurfaces in P£. The discriminant curve of such a net is a plane quintic which is the union of a non-singular quartic F and a line L. Moreover, F is endowed (in a natural way) with a non-effective theta characteristic n (that is, an invertible sheaf rj on F such that rj = Q. and h°(F, rj) = 0). One can associate to C the triple (F,rj;L), and the http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the London Mathematical Society Wiley

The Rationality of the Moduli Space of Bielliptic Curves of Genus Five

Loading next page...
 
/lp/wiley/the-rationality-of-the-moduli-space-of-bielliptic-curves-of-genus-five-CdsOLKjzxr

References (13)

Publisher
Wiley
Copyright
© London Mathematical Society
ISSN
0024-6093
eISSN
1469-2120
DOI
10.1112/blms/28.4.356
Publisher site
See Article on Publisher Site

Abstract

THE RATIONALITY OF THE MODULI SPACE OF BIELLIPTIC CURVES OF GENUS FIVE G. CASNATI AND A. DEL CENTINA 0. Introduction and notation Let C be an irreducible, smooth, projective curve of genus g ^ 2, defined over the complex field C, and let yjl be the coarse moduli space of smooth curves of genus g. C is called bielliptic if it admits a degree 2 morphism n.C^E onto an elliptic curve E. We denote by 9CR£ c yjl the moduli space of bielliptic curves of genus g. The aim of this paper is to present a proof of the following. THEOREM 0.1. 9W£ is rational. For this we proceed as follows. If [CJeSK!? , then the canonical model C of C is the base locus of a net of quadric hypersurfaces in P£. The discriminant curve of such a net is a plane quintic which is the union of a non-singular quartic F and a line L. Moreover, F is endowed (in a natural way) with a non-effective theta characteristic n (that is, an invertible sheaf rj on F such that rj = Q. and h°(F, rj) = 0). One can associate to C the triple (F,rj;L), and the

Journal

Bulletin of the London Mathematical SocietyWiley

Published: Jun 1, 1996

There are no references for this article.