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Integration of meromorphic cohomology classes and incidence divisors. (Intégration de classes de cohomologie méromorphes et diviseurs d’incidence.) (French) Zbl 0963.32019

Summary: The first goal of this paper is to generalize in local complex geometry the main idea in W. L. Chow and B. L. van der Waerden’ construction [Math. Ann. 113, 692-704 (1937; Zbl 0016.04004)]: associating the “incidence divisor” of a cycle with a given analytic family of cycles (the linear projective varieties of suitable dimension in the case of \(\mathbb{P}_N (\mathbb{C}))\).
Under very general hypotheses we associate a Cartier divisor on the parameter space in which arbitrary singularities are allowed to a local complete intersection.
The second goal is to study the singularities of functions obtained by integration of meromorphic cohomology classes on an analytic family of cycles. Our result enables us to control the pole order of the meromorphic functions on the parameter space from the pole order of the given cohomology class.

MSC:

32S60 Stratifications; constructible sheaves; intersection cohomology (complex-analytic aspects)
14M10 Complete intersections

Citations:

Zbl 0016.04004
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References:

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