The moduli space of genus four double covers of elliptic curves is rational

Fabio Bardelli and Andrea Del Centina

Vol. 144 (1990), No. 2, 219–227

DOI: 10.2140/pjm.1990.144.219

Abstract

This paper is devoted to a proof of the rationality of the moduli space of those genus four smooth complex projective curves which are double covers of some elliptic curve. The study of the canonical model of a genus four curve as above allows to reduce the initial moduli problem to a simple one in plane projective geometry; this last formulation leads to compute an explicit representation of a certain group on a vector space and its corresponding field of invariants.

Mathematical Subject Classification 2000

Primary: 14H10

Secondary: 14H30, 14H52

Milestones

Received: 12 August 1987

Published: 1 August 1990