The ∂¯ -equation on a non-reduced analytic space
Journal article, 2019

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.

Author

Mats Andersson

University of Gothenburg

Chalmers, Mathematical Sciences, Algebra and geometry

Richard Lärkäng

University of Gothenburg

Chalmers, Mathematical Sciences, Algebra and geometry

Mathematische Annalen

0025-5831 (ISSN) 1432-1807 (eISSN)

Vol. 374 1-2 553-599

Subject Categories

Algebra and Logic

Geometry

Mathematical Analysis

Roots

Basic sciences

DOI

10.1007/s00208-018-1678-8

More information

Latest update

7/16/2019