Let be a complex analytic space and be an isolated singular point of . We define the -th punctured local holomorphic de Rham cohomology to be the direct limit of where runs over strongly pseudoconvex neighborhoods of in , and is the holomorphic de Rahm cohomology of the complex manifold . We prove that punctured local holomorphic de Rham cohomology is an important local invariant which can be used to tell when the singularity is quasi-homogeneous. We also define and compute various Poincaré number and of isolated hypersurface singularity .
"Punctured local holomorphic de Rham cohomology." J. Math. Soc. Japan 55 (3) 633 - 640, July, 2003. https://doi.org/10.2969/jmsj/1191418993