L’obstruction d’Euler locale d’une application

Abstract

Our objective is to present a generalization for the local Euler obstruction of a holomorphic function singular at the origin to the case of a holomorphic map f:(V,0)→(ℂ k ,0), where (V, 0) is a germ of complex analytic variety, equidimensional of dimension n≥k. The principal result (Theorem 6.1) is a formula which computes the local Euler obstruction, defined for k-frames by Brasselet, Seade, Suwa, in terms of the local Euler obstruction of f.