A Dolbeault-Grothendieck lemma on complex spaces via Koppelman formulas

Details A Dolbeault-Grothendieck lemma on complex spaces via Koppelman formulas A Dolbeault-Grothendieck lemma on complex spaces via Koppelman formulas

2010-10-29

arxiv.org/abs/1010.6142v2

Mathematics

Complex Variables

Scientific paper

Let $X$ be a complex space of pure dimension. We introduce fine sheaves
$\A^X_q$ of $(0,q)$-currents, which coincides with the sheaves of smooth forms
on the regular part of $X$, so that the associated Dolbeault complex yields a
resolution of the structure sheaf $\hol^X$. Our construction is based on
intrinsic and quite explicit semi-global Koppelman formulas.

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