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 ∂ ̄ .
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