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

Elkik, R.

Ann. Sci. Éc. Norm. Supér. (4) 22, No. 2, 195-226 (1989).

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

References:

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