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.