Incidence Divisor

Abstract

The aim of this paper is to prove an important generalization of the construction of the Incidence Divisor given in [BMg]. Let Z be a complex manifold and (X_{s})_{s\in S}an family of n-cycles (not necessarily compact) in Z parametrized by reduced complex space S. Then, to any n+1- codimensional cycle Y in Z wich satisfies the following condition : the analytic set (S\times |Y|)\cap |X| in S\times Z is S-proper and generically finite on its image |\Sigma_{Y}| wich is nowhere dense in S, is associated a Cartier Divisor \Sigma_{Y} with support |\Sigma_{Y}|. Nice functorial properties of this correspondance are proven and we deduce the intersection number of this divisor with a curve in S.