The {\L}ojasiewicz exponent of nondegenerate surface singularities

TL;DR

This paper provides estimations and exact formulas for the {}ojasiewicz exponent of nondegenerate surface singularities using Newton diagrams, improving previous inequalities and generalizing known theorems.

Contribution

It introduces new estimations and exact formulas for the {}ojasiewicz exponent, extending previous results and generalizing the Lenarcik theorem to higher dimensions.

Findings

Stronger bounds than Fukui inequality.

Exact formulas in special cases.

Multidimensional generalization of Lenarcik theorem.

Abstract

In the article we give some estimations of the {\L}ojasiewicz exponent of nondegenerate surface singularities in terms of their Newton diagrams. We also give an exact formula for the {\L}ojasiewicz exponent of such singularities in some special cases. The results are stronger than Fukui inequality [8]. It is also a multidimensional generalization of the Lenarcik theorem [13].