Quelques remarques sur la géométrie des espaces conormaux. (Some remarks on the geometry of conormal spaces). (French) Zbl 0598.32011

Systèmes différentiels et singularités, Colloq. Luminy/France 1983, Astérisque 130, 161-192 (1985).
[For the entire collection see Zbl 0559.00004.]
Let X be a reduced analytic space, and let Z(X) be the group of analytic cycles on X. According to R. MacPherson, there is an isomorphism between Z(X) and the group F(X) of constructible functions with integral values on X, associating to a cycle z the function \(x\mapsto Eu_ z(x)=(- 1)^{\dim z}Eu_ z(x)\), where Eu is the local Euler obstruction [cf. R. MacPherson, Ann. Math., II. Ser. 100, 423-432 (1974; Zbl 0311.14001)]. In the paper under review the author uses this isomorphism and the Whitney stratification to describe certain geometric constructions, such as the direct and inverse images and specialization.
Reviewer: F.L.Zak


32S05 Local complex singularities
32S60 Stratifications; constructible sheaves; intersection cohomology (complex-analytic aspects)
14C15 (Equivariant) Chow groups and rings; motives
32C20 Normal analytic spaces