Brasselet number and Newton polygons

Abstract

We present a formula to compute the Brasselet number of f : (Y, 0) → (C, 0) where Y ⊂ X is a non-degenerate complete intersection in a toric variety X. As applications we establish several results concerning invariance of the Brasselet number for families of non-degenerate complete intersections. Moreover, when (X, 0) = (C n , 0) we derive sufficient conditions to obtain the invariance of the Euler obstruction for families of complete intersections with an isolated singularity which are contained in X.

Euler obstruction, Brasselet number and critical points

“…The reader may refer to [9,32] for further works on the Brasselet number. In the rest of the paper, we will explain how to obtain a result in the spirit of the result of Seade, Tibȃr and Verjovsky mentioned above, i.e.…”

Local topology of a deformation of a function-germ with a one-dimensional critical set

“…In [5], Dalbelo e Pereira provided formulas to compute the Brasselet number of a function defined over a toric variety and in [1], Ament, Nuño-Ballesteros, Oréfice-Okamoto and Tomazella computed the Brasselet number of a function-germ with isolated singularity at the origin and defined over an isolated determinantal variety (IDS) and the Brasselet number of finite functions defined over a reduced curve. More recently, in [4], Dalbelo and Hartmann calculated the Brasselet number of a function-germ defined over a toric variety using combinatorical properties of the Newton polygons. In the global study of the topology of a function germ, Dutertre and Grulha defined, in [7], the global Brasselet numbers and the Brasselet numbers at infinity.…”