Abelian varieties in Brill-Noether loci

In this paper, improving on results of Abramovich, Harris, Debarre and Fahlaoui [1], [8], we give the full classification of curves C of genus g such that a Brill-Noether locus Wds(C), strictly contained in the jacobian J(C) of C, contains a variety Z stable under translations by the elements of a positive dimensional abelian subvariety A⊊J(C) and such that dim(Z)=d−dim(A)−2s, i.e., the maximum possible for such a Z.