Sur certains faisceaux de formes m\'eromorphes en g\'eom\'etrie analytique complexe II

TL;DR

This paper investigates the functorial properties of sheaves of meromorphic forms on complex spaces, focusing on their extension, pullback, and higher direct images, especially in relation to desingularizations.

Contribution

It provides new insights into the behavior of meromorphic form sheaves under various morphisms and desingularizations in complex analytic geometry.

Findings

Meromorphic forms extend holomorphically on desingularizations.

Analysis of pull-back and higher direct image functors.

Results applicable to integration over fibers in complex spaces.

Abstract

We study some functorial properties of certain sheaves of meromorphic forms on reduced complex space; particulary, the meromorphic forms which extend holomorphicaly on any desingularisation. The purpose concern their behavior under pull back and higher direct image (and in some case by integration on fibres of equidimensional or open morphism).