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Polar Homology

Published online by Cambridge University Press:  20 November 2018

Boris Khesin  and
Alexei Rosly
Boris Khesin
Affiliation:
Department of Mathematics, University of Toronto, Toronto, Ontario, M5S 3G3 e-mail: khesin@math.toronto.edu
Alexei Rosly
Affiliation:
Institute of Theoretical and Experimental Physics, B. Cheremushkinskaya 25, 117259 Moscow, Russia e-mail: rosly@heron.itep.ru
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Abstract

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For complex projective manifolds we introduce polar homology groups, which are holomorphic analogues of the homology groups in topology. The polar $k$-chains are subvarieties of complex dimension $k$ with meromorphic forms on them, while the boundary operator is defined by taking the polar divisor and the Poincaré residue on it. One can also define the corresponding analogues for the intersection and linking numbers of complex submanifolds, which have the properties similar to those of the corresponding topological notions.

Keywords

Primary:14C1014F10secondary:58A14Poincaré residueholomorphic linking
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 55 , Issue 5 , 01 October 2003 , pp. 1100 - 1120
Copyright
Copyright © Canadian Mathematical Society 2003

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