Journal of the Mathematical Society of Japan
- J. Math. Soc. Japan
- Volume 55, Number 3 (2003), 633-640.
Punctured local holomorphic de Rham cohomology
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 .
J. Math. Soc. Japan, Volume 55, Number 3 (2003), 633-640.
First available in Project Euclid: 3 October 2007
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Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 14B05: Singularities [See also 14E15, 14H20, 14J17, 32Sxx, 58Kxx] 14B15: Local cohomology [See also 13D45, 32C36] 32S05: Local singularities [See also 14J17] 32S10: Invariants of analytic local rings 32S25: Surface and hypersurface singularities [See also 14J17]
HUANG, Xiaojun; Sun LUK, Hing; S.-T. YAU, Stephen. Punctured local holomorphic de Rham cohomology. J. Math. Soc. Japan 55 (2003), no. 3, 633--640. doi:10.2969/jmsj/1191418993. https://projecteuclid.org/euclid.jmsj/1191418993