# The sheaf α • X

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1 Géométrie IECL - Institut Élie Cartan de Lorraine 2 IUF - Institut Universitaire de France

Abstract : We introduce in a reduced complex space, a new coherent sub-sheaf- of the sheaf $\omega {X}^{\bullet}$ which has the universal pull-back property- for any holomorphic map, and which is in general bigger than the usual sheaf of holomorphic differential forms $\Omega {X}^{\bullet}-torsion$. We show that the meromorphic differential forms which are sections of this sheaf satisfy integral dependence equations over the symmetric algebra of the sheaf $\Omega {X}^{\bullet}-torsion$. This sheaf $\alpha {X}^{\bullet}$ is also closely related to the normalized Nash transform.\\We also show that these $q-$meromorphic differential forms are locally square-integrable on {\bf any} $q-$dimensional cycle in $X$ and that the corresponding functions obtained by integration on an analytic family of $q-$cycles are locally bounded and locally continuous on the complement of closed analytic subset.

Keywords : Meromorphic differential forms on a singular space Universal pull-back property Normalized Nash transform Integral dependence equation for differential forms.

Autor: Daniel Barlet -

Fuente: https://hal.archives-ouvertes.fr/

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