On Bochner-Martinelli residue currents and their annihilator ideals
[Sur les courants résiduels de type Bochner-Martinelli et leurs idéaux annihilateurs]
Jonsson, Mattias ; Wulcan, Elizabeth
Annales de l'Institut Fourier, Tome 59 (2009), p. 2119-2142 / Harvested from Numdam
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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 0∈C 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 0∈C 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).

Publié le : 2009-01-01
DOI : https://doi.org/10.5802/aif.2485
Classification:  32A26,  32A27,  32S45
Mots clés: courant résiduel, idéal annihilateur, valuation de Rees 
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     author = {Jonsson, Mattias and Wulcan, Elizabeth},
     title = {On Bochner-Martinelli residue currents and their annihilator ideals},
     journal = {Annales de l'Institut Fourier},
     volume = {59},
     year = {2009},
     pages = {2119-2142},
     doi = {10.5802/aif.2485},
     zbl = {1189.32003},
     mrnumber = {2640915},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_2009__59_6_2119_0}
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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) pp. 2119-2142. doi : 10.5802/aif.2485. http://gdmltest.u-ga.fr/item/AIF_2009__59_6_2119_0/

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