Lojasiewicz exponent of a surface: an intrinsic view

Abstract

In this paper we observe that the {\L}ojasiewicz 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 {\L}ojasiewicz exponent to rational singularities of higher multiplicities we make a similar observation for RTP-type singularities.