The ∂¯ -equation on a non-reduced analytic space

Journal article, 2019

Let X be a, possibly non-reduced, analytic space of pure dimension. We introduce a notion of ∂¯ -equation on X and prove a Dolbeault–Grothendieck lemma. We obtain fine sheaves AXq of (0, q)-currents, so that the associated Dolbeault complex yields a resolution of the structure sheaf OX. Our construction is based on intrinsic semi-global Koppelman formulas on X.