  We study tori attached to the fundamental groups of plane curves with
arbitrary singularities. These tori provide complete information about homology
of finite abelian covers of the plane branched along the curve. We calculate
these tori in terms of certain linear systems determined by the singularities
of the curve. In the case of the complements to a union of lines they can be
calculated from the lattice of the arrangement and are closely related to the
components of the space of Aomoto complexes with prescribed homology.
