The Łojasiewicz exponent of nondegenerate surface singularities

Abstract

AbstractLet f be an isolated singularity at the origin of $\mathbb {C}^n$ . One of many invariants that can be associated with f is its Łojasiewicz exponent $\mathcal {L}_0 (f)$ , which measures, to some extent, the topology of f. We give, for generic surface singularities f, an effective formula for $\mathcal {L}_0 (f)$ in terms of the Newton polyhedron of f. This is a realization of one of Arnold’s postulates.