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A Polar de Rham Theorem

B. Khesin·A. Rosly·R. P. Thomas
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Abstract

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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B. Khesin, A. Rosly, R. P. Thomas. 2003-10-27. A Polar de Rham Theorem. https://arxiv.org/abs/math/0305081

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