  In this paper, improving on results of Abramovich- Harris and Debarre-
Fahlaoui we give the full classification of curves C of genus g such that a
Brill--Noether locus W^ s_d(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 contained in J(C) and such that
dim(Z)=d-dim(A)-2s, i.e., the maximum possible for such a Z.
