Punctured local holomorphic de Rham cohomology

Let V be a complex analytic space and x be an isolated singular point of V. We define the q-th punctured local holomorphic de Rham cohomology H^q_h(V, x) to be the direct limit of H^q_h(U - (x)) where U runs over strongly pseudoconvex neighborhoods of x in V, and H^q_h(U - (x)) is the holomorphic de Rahm cohomology of the complex manifold U - (x). We prove that punctured local holomorphic de Rham cohomology is an important local invariant which can be used to tell when the singularity (V, x) is quasi-homogeneous. We also define and compute various Poincaré number p^-(i)_x and p^-(i)_x of isolated hypersurface singularity (V, x).