Limit spectral distribution for non-degenerate hypersurface singularities

TL;DR

This paper proves a continuous limit distribution for the spectrum of certain hypersurface singularities, explores bounds involving the log canonical threshold and Milnor number, and demonstrates the sharpness of these bounds.

Contribution

It establishes the limit spectral distribution for Newton non-degenerate hypersurface singularities and analyzes bounds related to the log canonical threshold and Milnor number.

Findings

Proves the limit distribution for the spectrum of hypersurface singularities.

Shows the log canonical threshold is bounded below by twice the inverse of the Milnor number.

Demonstrates the bound is asymptotically sharp.

Abstract

We establish Kyoji Saito's continuous limit distribution for the spectrum of Newton non-degenerate hypersurface singularities. Investigating Saito's notion of dominant value in the case of irreducible plane curve singularities, we find that the log canonical threshold is strictly bounded below by the doubled inverse of the Milnor number. We show that this bound is asymptotically sharp.