  Integrals of the Pfaffian form over the nonsingular part of a projective
variety compute information closely related to the Mather-Chern class of the
variety and to other invariants such as the local Euler obstruction along
strata of its singular locus and, in the hypersurface case, Milnor numbers. We
obtain simple proofs of these formulas, recovering along the way several
classically known results.
