Lojasiewicz exponent of a surface: an intrinsic view

Abstract

In this paper we observe that the Łojasiewicz exponent ${\mathcal{L}}_0(X)$ of an ADE-type singularity $X$ can be computed by means of invariants of certain ideals in the local ring ${\mathcal{O}}_{X,0}$. After extending the notion of Łojasiewicz exponent to rational singularities of higher multiplicities we make a similar observation for RTP-type singularities.