  Cohomology support loci of rank one local systems of a smooth quasiprojective
complex algebraic variety are finite unions of torsion-translated complex
subtori of the character variety of the fundamental group. Tangent spaces of
the character variety are (partially) represented by logarithmic 1-forms. In
this paper, we give a relation between cohomology support loci and the natural
strata of 1-forms given by the dimension of the vanishing locus. This relation
generalizes the one for the projective case due to Green and Lazarsfeld and
also generalizes the partial relation due to Dimca in the quasi-projective
case.
