A polar de Rham theorem
For a complex manifold \(X\) one can define its polar homology \(HP_*(X)\) as the homology of the polar chain complex whose building blocks are pairs \((Y,\beta)\) with \(Y\) a subvariety in \(X\) and \(\beta\) a meromorphic top degree form on \(Y\) having a simple pole. For \(X\) projective, the authors identify the group \(HP_q (X)\) with the Dolbeault cohomology group \(H^{n,n-q} (X)\) for all integers \(q\). A relative version for a pair \((X,D)\) with \(D\) a normal crossing divisor in \(X\) is also obtained.
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