Direct images of semi-meromorphic currents
Annales de l'Institut Fourier, Volume 68 (2018) no. 2, pp. 875-900.

We introduce a calculus for the class ASM(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 ASM(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.

Nous introduisons un calcul pour la classe ASM(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 ASM(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.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/aif.3180
Classification: 32A26,  32A27,  32B15,  32C30
Keywords: residue current, semi-meromorphic current, analytic space, pseudomeromorphic current
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Andersson, Mats; Wulcan, Elizabeth. Direct images of semi-meromorphic currents. Annales de l'Institut Fourier, Volume 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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