On Bochner-Martinelli residue currents and their annihilator ideals
[Sur les courants résiduels de type Bochner-Martinelli et leurs idéaux annihilateurs]
Annales de l'Institut Fourier, Tome 59 (2009) no. 6, pp. 2119-2142.

Nous étudions le courant résiduel de type Bochner-Martinelli R f associé à un m-uple de germes de fonctions holomorphes f=(f 1 ,,f m ) définies à l’origine 0C n dont l’ensemble des zéros communs se réduit à 0. Nos résultats principaux sont : une description géométrique de R f en terme des valuations de Rees associées à l’idéal (f) engendré par f et la caractérisation du cas où l’idéal annihilateur de R f est égal à (f).

We study the residue current R f of Bochner-Martinelli type associated with a tuple f=(f 1 ,,f m ) of holomorphic germs at 0C n , whose common zero set equals the origin. Our main results are a geometric description of R f in terms of the Rees valuations associated with the ideal (f) generated by f and a characterization of when the annihilator ideal of R f equals (f).

DOI : 10.5802/aif.2485
Classification : 32A26, 32A27, 32S45
Keywords: Residue current, annihilator ideal, Rees valuation
Mot clés : courant résiduel, idéal annihilateur, valuation de Rees
Jonsson, Mattias 1 ; Wulcan, Elizabeth 1

1 University of Michigan Department of Mathematics Ann Arbor MI 48109-1043 (USA)
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Jonsson, Mattias; Wulcan, Elizabeth. On Bochner-Martinelli residue currents and their annihilator ideals. Annales de l'Institut Fourier, Tome 59 (2009) no. 6, pp. 2119-2142. doi : 10.5802/aif.2485. http://www.numdam.org/articles/10.5802/aif.2485/

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