Explicit Serre duality on complex spaces

Abstract

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 ${\mathcal{B}}_X^{n,q}$ of certain currents on $X$ of bidegree $(n,q)$, such that the Dolbeault complex $({\mathcal{B}}_X^{n,\bullet },\bar{\partial })$ becomes, in a certain sense, a dualizing complex. In particular, if $X$ is Cohen-Macaulay (e.g., Gorenstein or a complete intersection) then $({\mathcal{B}}_X^{n,\bullet },\bar{\partial })$ is an explicit fine resolution of the Grothendieck dualizing sheaf.

Final version

References in corpus (1)

• Pseudomeromorphic currents on subvarieties