The Łojasiewicz exponent of non-degenerate surface singularities

Abstract

Let $f$ 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.

16 pages, 3 figures