Punctured local holomorphic de Rham cohomology

Xiaojun Huang, Hing Sun Luk, Stephen S.T. Yau

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

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 Hqh(V, x) to be the direct limit of Hqh(U - (x)) where U runs over strongly pseudoconvex neighborhoods of x in V, and Hqh(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 languageEnglish (US)
Pages (from-to)633-640
Number of pages8
JournalJournal of the Mathematical Society of Japan
Volume55
Issue number3
DOIs
StatePublished - 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

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