
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.
Mixed Hodge theory of singular varieties (complex-analytic aspects), Integral representations of solutions to PDEs, Chow Groups, Algebraic Cycles, Smooth
Mixed Hodge theory of singular varieties (complex-analytic aspects), Integral representations of solutions to PDEs, Chow Groups, Algebraic Cycles, Smooth
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