Minkowski Inequalities and non-isolated hypersurface singularities

TL;DR

This paper establishes new Minkowski-type inequalities involving Lê numbers for non-isolated hypersurface singularities, extending classical results and providing tools for understanding their geometric complexity.

Contribution

It introduces Minkowski inequalities for Lê numbers of non-isolated hypersurface singularities, generalizing existing inequalities for isolated cases.

Findings

Derived Lê-Iomdine formulas with inequalities

Established Minkowski inequalities for Lê numbers

Extended classical inequalities to non-isolated singularities

Abstract

We derive a number of inequalities involving L\^e numbers of non-isolated hypersurface singularities. In particular, we derive L\^e-Iomdine formulas with inequalities and use these, together with Teissier's Minkowski inequalities for sectional Milnor numbers of isolated hypersurface singularities, to arrive at ``Minkowski inequalities'' for L\^e numbers.