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arXiv · 1010.6142

A Dolbeault-Grothendieck lemma on complex spaces via Koppelman formulas

Mats Andersson·Håkan Samuelsson
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Abstract

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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Mats Andersson, Håkan Samuelsson. 2010-10-29. A Dolbeault-Grothendieck lemma on complex spaces via Koppelman formulas. https://arxiv.org/abs/1010.6142

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