A Polar de Rham Theorem

Details A Polar de Rham Theorem A Polar de Rham Theorem

2003-05-05

arxiv.org/abs/math/0305081v2

Topology Volume 43, Issue 5 (2004) Pages 1231-1246

Mathematics

Algebraic Geometry

Referee's corrections. 17 pages, to appear in Topology

Scientific paper

We prove an analogue of the de Rham theorem for polar homology; that the polar homology $HP_q(X)$ of a smooth projective variety $X$ is isomorphic to its $H^{n,n-q}$ 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 $\bar\partial$.

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