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Families of differential forms on complex spaces. (English) Zbl 1170.35358
Summary: On every reduced complex space \(X\) we construct a family of complexes of soft sheaves \(\Omega_X\); each of them is a resolution of the constant sheaf \(\mathbb{C}_X\) and induces the ordinary De Rham complex of differential forms on a dense open analytic subset of \(X\). The construction is functorial (in a suitable sense). Moreover each of the above complexes can fully describe the mixed Hodge structure of Deligne on a compact algebraic variety.

MSC:
35C15 Integral representations of solutions to PDEs
32S35 Mixed Hodge theory of singular varieties (complex-analytic aspects)
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