The dbar-equation on a non-reduced analytic space
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 ne sheaves Aq
X 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.