GV-subschemes and their embeddings in principally polarized abelian varieties

Abstract

We prove that the embedding of a $GV$-subscheme in a principally polarized abelian variety does not factor through any nontrivial isogeny. As an application, we present a new proof of a theorem of Clemens--Griffiths identifying the intermediate Jacobian of a smooth cubic threefold in ${\mathbf{P}}^4$ to the Albanese variety of its Fano surface of lines.

11 pages