Direct images of semi-meromorphic currents

Andersson, Mats; Wulcan, Elizabeth

doi:10.5802/aif.3180

Direct images of semi-meromorphic currents
[Images directes de courants semi-méromorphes]

Andersson, Mats ¹ ; Wulcan, Elizabeth ¹

¹ University of Gothenburg and Chalmers University of Technology, Department of Mathematical Sciences, Division of Mathematics, SE-412 96 Göteborg (Sweden)

Annales de l'Institut Fourier, Tome 68 (2018) no. 2, pp. 875-900.

Résumé
Abstract

Nous introduisons un calcul pour la classe $A S M (X)$ d’images directes de courants semi-méromorphes sur un espace analytique reduit $X$ , qui étend le calcul classique de Coleff, Herrera et Passare. Notre résultat principal montre que chaque élément de cette classe agit de manière analogue à une multiplication sur le faisceau ${𝒫ℳ}_{X}$ de courants pseudoméromorphes sur $X$ . Nous prouvons également que $A S M (X)$ ainsi que ${𝒫ℳ}_{X}$ et certains sous-faisceaux sont fermés sous l’action des opérateurs différentiels holomorphes et la multiplication intérieure par des champs vectoriels holomorphes.

We introduce a calculus for the class $A S M (X)$ of direct images of semi-meromorphic currents on a reduded analytic space $X$ , that extends the classical calculus due to Coleff, Herrera and Passare. Our main result is that each element in this class acts as a kind of multiplication on the sheaf ${𝒫ℳ}_{X}$ of pseudomeromorphic currents on $X$ . We also prove that $A S M (X)$ as well as ${𝒫ℳ}_{X}$ and certain subsheaves are closed under the action of holomorphic differential operators and interior multiplication by holomorphic vector fields.

Reçu le : 2016-12-07
Révisé le : 2017-09-11
Accepté le : 2017-09-14
Publié le : 2018-04-18

DOI : 10.5802/aif.3180

Classification : 32A26, 32A27, 32B15, 32C30
Keywords: residue current, semi-meromorphic current, analytic space, pseudomeromorphic current
Mot clés : courant résiduel, courant semi-méromorphe, espace analytique, courant pseudoméromorphe

Affiliations des auteurs :

Andersson, Mats ¹ ; Wulcan, Elizabeth ¹

¹ University of Gothenburg and Chalmers University of Technology, Department of Mathematical Sciences, Division of Mathematics, SE-412 96 Göteborg (Sweden)

Licence :

CC-BY-ND 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     title = {Direct images of semi-meromorphic currents},
     journal = {Annales de l'Institut Fourier},
     pages = {875--900},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
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     doi = {10.5802/aif.3180},
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Andersson, Mats; Wulcan, Elizabeth. Direct images of semi-meromorphic currents. Annales de l'Institut Fourier, Tome 68 (2018) no. 2, pp. 875-900. doi : 10.5802/aif.3180. https://aif.centre-mersenne.org/articles/10.5802/aif.3180/

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