Abstract:
We give an algorithm to compute the Lê numbers of (the germ of) a Newton non-degenerate complex analytic function f: (C^n,0) --> (C,0) in terms of certain invariants attached to the Newton diagram of the function f+z_1^{a_1}+...+z_d^{a_d}, where d is the dimension of the critical locus of f and a_1,...,a_d are sufficiently large integers. This is a version for non-isolated singularities of a famous theorem of A.G. Kouchnirenko. As a corollary, we obtain that Newton non-degenerate functions with the same Newton diagram have the same Lê numbers. This is a joint work with G. Oleksik and A. Rozycki.