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Zbl 0701.14003
Elkik, R.
Fibrés d'intersections et intégrales de classes de Chern. (Intersection bundles and integrals of Chern classes). (French)
[J] Ann. Sci. Éc. Norm. Supér. (4) 22, No. 2, 195-226 (1989). ISSN 0012-9593

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.
[J.H.de Boer]

MSC 2000:: *14C17 Intersection theory
14F05 Sheaves, etc.

Keywords: intersection line bundle; intersection sheaf; Chern classes

Cited in: Zbl 0870.14010

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