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Residue Currents and their Annihilator Ideals

Elizabeth Wulcan (Institutionen för matematiska vetenskaper, matematik)
Göteborg : Chalmers University of Technology, 2007. ISBN: 978-91-7291-922-8.- 149 s.
[Doktorsavhandling]

This thesis presents results in multidimensional residue theory. From a generically exact complex of locally free analytic sheaves $\mathcal C$ we construct a vector valued residue current $R^\mathcal C$, which in a sense measures the exactness of $\mathcal C$.

If $\mathcal C$ is a locally free resolution of the ideal (sheaf) $J$ the annihilator ideal of $R^\mathcal C$ is precisely $J$. This generalizes the Duality Theorem for Coleff-Herrera products of complete intersection ideals and can be used to extend several results, previously known for complete intersections.

We compute $R^\mathcal C$ explicitly if $\mathcal C$ is a so called cellular resolution of an Artinian monomial ideal $J$, and relate the structure of $R^\mathcal C$ to irreducible decompositions of $J$.

If $\mathcal C$ is the Koszul complex associated with a set of generators $f$ of the ideal $J$ the entries of $R^\mathcal C$ are the residue currents of Bochner-Martinelli type of $f$, which were introduced by Passare, Tsikh and Yger. We compute these in case $J$ is an Artinian monomial ideal and conclude that the corresponding annihilator ideal is strictly included in $J$, unless $J$ is a complete intersection.

We also define products of residue currents of Bochner-Martinelli type, generalizing the classical Coleff-Herrera product, and show that if $f$ defines a complete intersection the product of the residue currents of Bochner-Martinelli type of subtuples of $f$ coincides with the residue current of Bochner-Martinelli type of $f$.

Nyckelord: residue currents, Bochner-Martinelli formula, ideals of holomorphic functions, monomial ideals, coherents sheaves, free resolutions of modules, cellular resolutions



Denna post skapades 2007-04-05. Senast ändrad 2016-04-28.
CPL Pubid: 40389

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Matematik

Chalmers infrastruktur

Relaterade publikationer

Inkluderade delarbeten:


Noetherian Residue Currents


Products of residue currents of Cauchy-Fantappiè-Leray type


Residue currents of monomial ideals


Examination

Datum: 2007-05-11
Tid: 10:00
Lokal: Euler, Matematiska Vetenskaper, Chalmers Tvärgata 3, Chalmers tekniska högskola
Opponent: Mattias Jonsson, Department of Mathematics, University of Michigan, USA och Institutionen för matematik, KTH

Ingår i serie

Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie 2603