Direct images of semi-meromorphic currents

Andersson, Mats; Wulcan, Elizabeth

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

We introduce a calculus for the class $ASM\left(X\right)$ 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 ${\mathrm{𝒫ℳ}}_X$ of pseudomeromorphic currents on $X$. We also prove that $ASM\left(X\right)$ as well as ${\mathrm{𝒫ℳ}}_X$ 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 $ASM\left(X\right)$ 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 ${\mathrm{𝒫ℳ}}_X$ de courants pseudoméromorphes sur $X$. Nous prouvons également que $ASM\left(X\right)$ ainsi que ${\mathrm{𝒫ℳ}}_X$ et certains sous-faisceaux sont fermés sous l’action des opérateurs différentiels holomorphes et la multiplication intérieure par des champs vectoriels holomorphes.

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

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