## Abstract

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).

Original language | English (US) |
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Pages (from-to) | 633-640 |

Number of pages | 8 |

Journal | Journal of the Mathematical Society of Japan |

Volume | 55 |

Issue number | 3 |

DOIs | |

State | Published - 2003 |

## All Science Journal Classification (ASJC) codes

- Mathematics(all)

## Keywords

- Cohomology
- Holomorphic de Rham cohomology
- Isolated hypersurface singularity
- Milnor number
- Poincaré number
- Punctured local holomorphic de Rham