Work

The $$\bar{\partial }$$ ∂ ¯ -equation on a non-reduced analytic space

Year: 2018

Type: article

Abstract: Let X be a, possibly non-reduced, analytic space of pure dimension. We introduce a notion of $$\overline{\partial }$$ -equation on X and prove a Dolbeault–Grothendieck lemma. We obtain fine sheaves $$\mathcal {A}_X^q$$ of (0, q)-currents, so that the associated Dolbeault complex yields a resolution of the structure sheaf $$\mathscr {O}_X$$ . Our construction is based on intrinsic semi-global Koppelman formulas on X.

Source: Mathematische Annalen

DOI: 10.1007/s00208-018-1678-8

Authors: Mats Andersson, Richard Lärkäng

Institutions: Chalmers University of Technology, University of Gothenburg

Language: English

Topic: Geometry and complex manifolds

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funder: Vetenskapsrådet