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The (partial derivative)over-bar-equation on a non-reduced analytic space

Journal article
Authors Mats Andersson
Richard Lärkäng
Published in Mathematische Annalen
Volume 374
Issue 1-2
Pages 553-599
ISSN 0025-5831
Publication year 2019
Published at Department of Mathematical Sciences, Algebra and Geometry
Pages 553-599
Language en
Keywords Mathematics
Subject categories Mathematics


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.

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