A polar de Rham theorem

Boris Khesin, Alexei Rosly, Richard Thomas

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)

Abstract

We prove an analogue of the de Rham theorem for polar homology; that the polar homology HPq(X) of a smooth projective variety X is isomorphic to its Hn,n-q Dolbeault cohomology group. This analogue can be regarded as a geometric complexification where arbitrary (sub)manifolds are replaced by complex (sub)manifolds and de Rham's operator d is replaced by Dolbeault's ∂̄.

Original languageEnglish
Pages (from-to)1231-1246
Number of pages16
JournalTopology
Volume43
Issue number5
DOIs
Publication statusPublished - Sep 2004
Externally publishedYes

Keywords

  • Algebraic cycles
  • de Rham cohomology
  • Dolbeault cohomology
  • Hodge theory
  • Meromorphic forms

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