THE MODULI SPACE OF GENUS 4 DOUBLE COVERS OF ELLIPTIC-CURVES IS RATIONAL

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. © 1990 by Pacific Journal of Mathematics.