Théorie des résidus de Leray et formes de Barlet sur une intersection complète singulière

Abstract

Let S be a complex analytic manifold and C⊂ S a reduced complete intersection. We construct a complex Ω S •( logC) of sheaves of the so-called multi-logarithmic differential forms on S with respect to C and define a residue map res:Ω S •( logC)→ω C • from this complex onto the Barlet complex ω C • of regular meromorphic differential forms on C. The residue map is proved to be a natural morphism between the two complexes; it follows then that sections of the complex ω C • may be regarded as a generalization of the residue differential forms defined by Leray. Moreover, we show that the map res can be given explicitly in terms of a certain integration current.