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Residue Currents and their Annihilator Ideals

Författare och institution:
Elizabeth Wulcan (Institutionen för matematiska vetenskaper, matematik, Chalmers/GU)
Utgiven i serie vid Göteborgs universitet:
Doktorsavhandlingar vid Chalmers tekniska högskola. Ny serie, ISSN 0346-718X; nr 2603
ISBN:
978-91-7291-922-8
Antal sidor:
149
Publikationstyp:
Doktorsavhandling
Förlag:
Chalmers University of Technology
Förlagsort:
Göteborg
Publiceringsår:
2007
Språk:
engelska
Datum för examination:
2007-05-11
Tidpunkt för examination:
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
Inkluderade delarbeten:
Fulltextlänk:
Sammanfattning (abstract):

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 $f$.

Ämne (baseras på Högskoleverkets indelning av forskningsämnen):
NATURVETENSKAP ->
Matematik
Nyckelord:
residue currents, Bochner-Martinelli formula, ideals of holomorphic functions, monomial ideals, coherents sheaves, free resolutions of modules, cellular resolutions
Postens nummer:
40389
Posten skapad:
2007-04-05 14:24
Posten ändrad:
2016-04-28 09:57

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