A short proof of a formula of Brasselet, Lê and Seade for the Euler obstruction
نویسنده
چکیده
Theorem 0.1. Let (X, 0) be a germ of an equidimensional complex space (of positive dimension) in C . Let Vi, i = 1, · · · , k, be the (connected) strata of a Whitney stratification of a small representative X of (X, 0). Then there is an open dense Zariski subset Ω in the space of complex linear forms L on C , such that for every l ∈ Ω, there is ǫ0, such that for any ǫ, ǫ0 > ǫ > 0 and t0 sufficiently small, we have the following formula for the Euler obstruction of (X, 0):
منابع مشابه
Lê-Greuel type formula for the Euler obstruction and applications
The Euler obstruction of a function f can be viewed as a generalization of the Milnor number for functions defined on singular spaces. In this work, using the Euler obstruction of a function, we give a version of the Lê-Greuel formula for germs f : (X, 0) → (C, 0) and g : (X, 0) → (C, 0) of analytic functions with isolated singularity at the origin. Using this formula and results of Loeser, we ...
متن کاملIndex Formula for Macpherson Cycles of Affine Algebraic Varieties
We give explicit MacPherson cycles for the Chern-MacPherson class of a closed affine algebraic variety X and for any constructible function α with respect to a complex algebraic Whitney stratification of X . We define generalized degrees of the global polar varieties and of the MacPherson cycles and we prove a global index formula for the Euler characteristic of α. Whenever α is the Euler obstr...
متن کاملThe Multiplicity Polar Theorem and Isolated Singularities
Recently there has been much work done in the study of isolated singularities. The singularities may be those of sets, functions, vector fields or differential forms. Examples can be found in the references at the end of this paper. In these works the authors have developed algebraic invariants which describe the isolated singularity. In this paper, we show how many of these invariants can be c...
متن کاملA SHORT PROOF FOR THE EXISTENCE OF HAAR MEASURE ON COMMUTATIVE HYPERGROUPS
In this short note, we have given a short proof for the existence of the Haar measure on commutative locally compact hypergroups based on functional analysis methods by using Markov-Kakutani fixed point theorem.
متن کاملA short proof of the maximum conjecture in CR dimension one
In this paper and by means of the extant results in the Tanaka theory, we present a very short proof in the specific case of CR dimension one for Beloshapka's maximum conjecture. Accordingly, we prove that each totally nondegenerate model of CR dimension one and length >= 3 has rigidity. As a result, we observe that the group of CR automorphisms associated with each of such models contains onl...
متن کامل