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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
Bulletin of the London Mathematical Society – Wiley
Published: Jun 1, 1996
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