  We study the 0-th local cohomology module of the jacobian ring of a singular
reduced complex projective hypersurface X, by relating it to the sheaf of
logarithmic vector field along X. We investigate the analogies between the
local cohomology and the well known properties of the jacobian ring of a
nonsingular hypersurface. In particular we study self-duality, Hodge theoretic
and Torelli type questions.
