Brasselet number and Newton polygons

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 .