Polar Homology

Boris Khesin, Alexei Rosly

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)1100-1120
Number of pages21
JournalCanadian Journal of Mathematics
Issue number5
Publication statusPublished - Oct 2003
Externally publishedYes


  • Holomorphic linking
  • Poincaré residue


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