  We investigate the relations between the syzygies of the Jacobian ideal of
the defining equation for a projective hypersurface $V$ with isolated
singularities and the Torelli properties of $V$ (in the sense of
Dolgachev-Kapranov). We show in particular that hypersurfaces with a small
Tjurina numbers are Torelli in this sense. When $V$ is a plane curve, or more
interestingly, a surface in $P^3$, we discuss the stability of the reflexive
sheaf of logarithmic vector fields along $V$. A new lower bound for the minimal
degree of a syzygy associated to a 1-dimensional complete intersection is also
given.
