Uniqueness and factorization of Coleff-Herrera currents
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 18 (2009) no. 4, p. 651-661

We prove a uniqueness result for Coleff-Herrera currents which in particular means that if f=(f 1 ,...,f m ) defines a complete intersection, then the classical Coleff-Herrera product associated to f is the unique Coleff-Herrera current that is cohomologous to 1 with respect to the operator δ f - ¯, where δ f is interior multiplication with f. From the uniqueness result we deduce that any Coleff-Herrera current on a variety Z is a finite sum of products of residue currents with support on Z and holomorphic forms.

Nous prouvons un résultat d’unicité pour les courants de Coleff-Herrera qui dit en particulier que si f=(f 1 ,,f n ) définit une intersection complète, alors le produit de Coleff-Herrera classique associé à f est le seul courant de Coleff-Herrera qui soit cohomologue à 1 pour l’opérateur δ f - ¯, où δ f est le produit intérieur par f. De ce résultat d’unicité, nous déduisons que tout courant de Coleff-Herrera sur une variété Z est une somme finie de produits de courants résiduels supportés sur Z par des formes holomorphes.

@article{AFST_2009_6_18_4_651_0,
     author = {Andersson, Mats},
     title = {Uniqueness and factorization of Coleff-Herrera currents},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 18},
     number = {4},
     year = {2009},
     pages = {651-661},
     doi = {10.5802/afst.1219},
     mrnumber = {2590383},
     zbl = {1187.32026},
     language = {en},
     url = {http://www.numdam.org/item/AFST_2009_6_18_4_651_0}
}
Andersson, Mats. Uniqueness and factorization of Coleff-Herrera currents. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 18 (2009) no. 4, pp. 651-661. doi : 10.5802/afst.1219. http://www.numdam.org/item/AFST_2009_6_18_4_651_0/

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