Isogenies of Jacobians

Abstract

We prove by means of the study of the infinitesimal variation of Hodge structure and a generalization of the classical Babbage-Enriques-Petri theorem that the Jacobian variety of a generic element of a $k$ codimensional subvariety of ${\mathcal{M}}_g$ is not isogenous to a distinct Jacobian if $g>3k+4$. We extend this result to $k=1,g\ge 5$ by using degeneration methods.

Final version with minor corrections. To appear in Algebraic Geometry

Cited by in corpus (1)

• On isogenies of Prym varieties