Atsushi Ikeda (Tokyo Denki University)

Prym-Torelli theorem for double coverings of elliptic curves

Abstract

Prym variety is a polarized abelian variety of dimension d=d(g,n) constructed from a double covering of a nonsingular projective curve of genus g branched at 2n points. The construction defines the Prym map from the moduli space R(g,n) of the double coverings to the moduli space A(d) of polarized abelian varieties. We discuss the injectivity of the Prym map when the dimension of R(g,n) is not grater than the dimension of A(d). It is known that the Prym map is generically injective, but it is not injective in general. In this talk, we state that the Prym map is injective for g=1, and explain how the double covering of the elliptic curve is reconstructed from the polarized abelian variety.