A regularisation of the Coleff–Herrera residue current

Håkan Samuelsson

doi:10.1016/j.crma.2004.06.003

Complex Analysis

A regularisation of the Coleff–Herrera residue current
[Une régularisation du courant résiduel de Coleff–Herrera.]

Présenté par : Pierre Lelong

Håkan Samuelsson ¹

¹ Matematik, Chalmers tekniska högskola och Göteborgs universitet, 41296 Göteborg, Sweden

Comptes Rendus. Mathématique, Volume 339 (2004) no. 4, pp. 245-250.

Résumé
Abstract

Nous démontrons que, si une application holomorphe d'une variété complexe à valeurs dans $C^{2}$ définit une intersection complète, alors le courant résiduel de Coleff–Herrera correspondant peut être régularisé par une $(0, 2)$ -forme dépendant de deux paramètres.

We prove that if a holomorphic mapping from some complex manifold to $C^{2}$ defines a complete intersection then the corresponding Coleff–Herrera residue current can be smoothly regularised by a $(0, 2)$ -form depending on two parameters.

Reçu le : 2004-05-12
Accepté le : 2004-06-01
Publié le : 2004-07-28

DOI : 10.1016/j.crma.2004.06.003

Affiliations des auteurs :

Håkan Samuelsson ¹

¹ Matematik, Chalmers tekniska högskola och Göteborgs universitet, 41296 Göteborg, Sweden

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Håkan Samuelsson. A regularisation of the Coleff–Herrera residue current. Comptes Rendus. Mathématique, Volume 339 (2004) no. 4, pp. 245-250. doi : 10.1016/j.crma.2004.06.003. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.06.003/

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