Limit distribution of Hodge spectral exponents of irreducible plane curve singularities

TL;DR

This paper investigates the distribution of Hodge spectral exponents for irreducible plane curve singularities, providing formulas, characterizations, and intervals for their limit distributions compared to continuous models.

Contribution

It offers a closed-form formula for the difference in distributions and characterizes families of curves with specific limit behaviors.

Findings

Derived a closed formula for distribution differences

Characterized curve families with continuous limit distributions

Identified intervals of dominating values for spectral exponents

Abstract

We study the distribution of the Hodge spectral exponents of an irreducible plane curve by comparing it with a continuous distribution. We provide a closed formula for this difference in terms of numerical invariants of the curve. We characterize those families of irreducible plane curves whose limit distribution of Hodge spectral exponents is the continuous distribution and we provide intervals of dominating values.