Open Access
July, 2003 Punctured local holomorphic de Rham cohomology
Xiaojun HUANG, Hing Sun LUK, Stephen S.-T. YAU
J. Math. Soc. Japan 55(3): 633-640 (July, 2003). DOI: 10.2969/jmsj/1191418993


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 Hhq(V,x) to be the direct limit of Hhq(U-{x}) where U runs over strongly pseudoconvex neighborhoods of x in V, and Hhq(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˜x(i) and p¯x(i) of isolated hypersurface singularity (V,x).


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Xiaojun HUANG. Hing Sun LUK. Stephen S.-T. YAU. "Punctured local holomorphic de Rham cohomology." J. Math. Soc. Japan 55 (3) 633 - 640, July, 2003.


Published: July, 2003
First available in Project Euclid: 3 October 2007

zbMATH: 1034.32018
MathSciNet: MR1978213
Digital Object Identifier: 10.2969/jmsj/1191418993

Primary: 14B05 , 14B15 , 32S05 , 32S10 , 32S25

Keywords: Holomorphic de Rham cohomology , Isolated hypersurface singularity , Milnor number , Poincar\'{e} number , Punctured local holomorphic de Rham cohomology

Rights: Copyright © 2003 Mathematical Society of Japan

Vol.55 • No. 3 • July, 2003
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