On Bochner-Martinelli residue currents and their annihilator ideals
Annales de l'Institut Fourier, Volume 59 (2009) no. 6, p. 2119-2142

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).

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).

DOI : https://doi.org/10.5802/aif.2485
Classification:  32A26,  32A27,  32S45
Keywords: Residue current, annihilator ideal, Rees valuation
@article{AIF_2009__59_6_2119_0,
     author = {Jonsson, Mattias and Wulcan, Elizabeth},
     title = {On Bochner-Martinelli residue currents and their annihilator ideals},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {59},
     number = {6},
     year = {2009},
     pages = {2119-2142},
     doi = {10.5802/aif.2485},
     mrnumber = {2640915},
     zbl = {1189.32003},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2009__59_6_2119_0}
}
Jonsson, Mattias; Wulcan, Elizabeth. On Bochner-Martinelli residue currents and their annihilator ideals. Annales de l'Institut Fourier, Volume 59 (2009) no. 6, pp. 2119-2142. doi : 10.5802/aif.2485. http://www.numdam.org/item/AIF_2009__59_6_2119_0/

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