Lê numbers and Newton diagram

Abstract

We give an algorithm to compute the Lê numbers of (the germ of) a Newton non-degenerate complex analytic function f:(Cn,0)→(C,0) in terms of certain invariants attached to the Newton diagram of the function f+z1α1+⋯+zdαd, where d is the dimension of the critical locus of f and α1,…,αd 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.