Abstract
Let X be a complex space of pure dimension. We introduce fine sheaves 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 . Our construction is based on intrinsic and quite explicit semi-global Koppelman formulas.
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The first author was partially supported by a grant from the Swedish Research Council. The second author wishes to thank the Department of Mathematics, University of Oslo, where part of his work was done.
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Andersson, M., Samuelsson, H. A Dolbeault-Grothendieck lemma on complex spaces via Koppelman formulas. Invent. math. 190, 261–297 (2012). https://doi.org/10.1007/s00222-012-0380-9
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DOI: https://doi.org/10.1007/s00222-012-0380-9