The Yau's characterization of isolated homogeneous hypersurface singularities

TL;DR

This paper provides a straightforward proof of Yau's characterization of isolated homogeneous hypersurface singularities using the semicontinuity of the Milnor number and the Łojasiewicz exponent.

Contribution

It offers a simplified proof of a key characterization in singularity theory, enhancing understanding of hypersurface singularities.

Findings

Proof of Yau's characterization using semicontinuity properties

Clarification of the role of Milnor number and Łojasiewicz exponent

Simplification of existing theoretical results

Abstract

Using the semicontinuity of the Milnor number and the {\L}ojasiewicz exponent, we give a simple proof of Yau's characterization of isolated homogenous hypersurface singularities.