Mathematics > Complex Variables
[Submitted on 18 Feb 2009 (v1), last revised 23 Aug 2011 (this version, v2)]
Title:Coleff-Herrera currents, duality, and Noetherian operators
View PDFAbstract:Let $\I$ be a coherent subsheaf of a locally free sheaf $\Ok(E_0)$ and suppose that $\F=\Ok(E_0)/\I$ has pure codimension. Starting with a residue current $R$ obtained from a locally free resolution of $\F$ we construct a vector-valued Coleff-Herrera current $\mu$ with support on the variety associated to $\F$ such that $\phi$ is in $\I$ if and only if $\mu\phi=0$. Such a current $\mu$ can also be derived algebraically from a fundamental theorem of Roos about the bidualizing functor, and the relation between these two approaches is discussed. By a construction due to Björk one gets Noetherian operators for $\I$ from the current $\mu$. The current $R$ also provides an explicit realization of the Dickenstein-Sessa decomposition and other related canonical isomorphisms.
Submission history
From: Mats Andersson [view email][v1] Wed, 18 Feb 2009 07:44:31 UTC (20 KB)
[v2] Tue, 23 Aug 2011 08:12:19 UTC (20 KB)
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