The {\L}ojasiewicz exponent for weighted homogeneous polynomial with isolated singularity

TL;DR

This paper derives an explicit formula for the { extL}ojasiewicz exponent of isolated weighted homogeneous singularities based on their weights, providing a precise mathematical characterization.

Contribution

It introduces a new explicit formula linking the { extL}ojasiewicz exponent to the weights of weighted homogeneous singularities, advancing understanding of their geometric properties.

Findings

Derived an explicit formula for the { extL}ojasiewicz exponent

Connected the exponent to the weights of the singularity

Enhanced mathematical understanding of weighted homogeneous singularities

Abstract

The purpose of this paper is to give an explicit formula of the {\L}ojasiewicz exponent of an isolated weighted homogeneous singularity in terms of its weights.