On Bochner-Martinelli residue currents and their annihilator ideals

Jonsson, Mattias; Wulcan, Elizabeth

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 $f=(f_1,\cdots ,f_m)$ définies à l’origine $0\in {\mathbf{C}}^n$ 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 $\left(f\right)$ engendré par f et la caractérisation du cas où l’idéal annihilateur de $R^f$ est égal à $\left(f\right)$.

We study the residue current $R^f$ of Bochner-Martinelli type associated with a tuple $f=(f_1,\cdots ,f_m)$ of holomorphic germs at $0\in {\mathbf{C}}^n$, 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 $\left(f\right)$ generated by $f$ and a characterization of when the annihilator ideal of $R^f$ equals $\left(f\right)$.

Classification : 32A26, 32A27, 32S45
Keywords: Residue current, annihilator ideal, Rees valuation
Mot clés : courant résiduel, idéal annihilateur, valuation de Rees

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