Incidence Divisor
Abstract
Description
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 |Σ_{Y}| wich is nowhere dense in S, is associated a Cartier Divisor Σ_{Y} with support |Σ_{Y}|. Nice functorial properties of this correspondance are proven and we deduce the intersection number of this divisor with a curve in S.
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