## Fibrés d’intersections et intégrales de classes de Chern. (Intersection bundles and integrals of Chern classes).(French)Zbl 0701.14003

Generalizing a definition given by Deligne in the case of a family of curves to the case of a morphism $$f: X\to S$$ of arbitrary dimension d, one defines the intersection sheaf relative to S of a set of $$d+1$$ given invertible sheaves on X. It is an invertible sheaf on S and it is also called the intersection sheaf of the product of the corresponding Chern classes, a notion that is extended to a product of degree $$d+1$$ of Chern classes of vector bundles on X, and then also called the integral along f of that product. Several general properties of the intersection sheaf are given, for instance a multiplicativity formula for a product involving a direct sum of two vector bundles.
Reviewer: J.H.de Boer

### MSC:

 14C17 Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry 14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)

### Keywords:

intersection line bundle; intersection sheaf; Chern classes
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### References:

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