Local cohomology of logarithmic forms
Let be a divisor on a smooth algebraic variety . We investigate the geometry of the Jacobian scheme of , homological invariants derived from logarithmic differential forms along , and their relationship with the property that be a free divisor. We consider arrangements of hyperplanes as a source of examples and counterexamples. In particular, we make a complete calculation of the local cohomology of logarithmic forms of generic hyperplane arrangements.