Explicit Serre duality on complex spaces
Journal article, 2017

In this paper we use recently developed calculus of residue currents together with integral formulas to give a new explicit analytic realization, as well as a new analytic proof of Serre duality on any reduced pure n-dimensional paracompact complex space X. At the core of the paper is the introduction of concrete fine sheaves $A^{n,q}_X$ of certain currents on X of bidegree (n,q), such that the corresponding Dolbeault complex becomes, in a certain sense, a dualizing complex. In particular, if X is Cohen-Macaulay (e.g., Gorenstein or a complete intersection) then this Dolbeault complex becomes an explicit fine resolution of the Grothendieck dualizing sheaf.


Jean Ruppenthal

Bergische Universität Wuppertal

Håkan Samuelsson Kalm

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

Elizabeth Wulcan

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

Advances in Mathematics

0001-8708 (ISSN) 1090-2082 (eISSN)

Vol. 305 1320-1355

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Mathematical Analysis


Basic sciences



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3/2/2018 9