Abstract

Let X be a, possibly non-reduced, analytic space of pure dimension. We introduce a notion of overline{partial }-equation on X and prove a Dolbeault–Grothendieck lemma. We obtain fine sheaves mathcal {A}_X^q of (0, q)-currents, so that the associated Dolbeault complex yields a resolution of the structure sheaf mathscr {O}_X. Our construction is based on intrinsic semi-global Koppelman formulas on X.

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