Spectrum of Projective Plane Curve Arrangements with Ordinary Singularities

TL;DR

This paper derives a combinatorial formula for the Hodge spectrum of projective plane curve arrangements with only ordinary singularities, expanding explicit calculations to a broader class of singularities.

Contribution

It provides the first explicit combinatorial formula for the Hodge spectrum of such arrangements with ordinary singularities.

Findings

Derived a combinatorial formula for the Hodge spectrum

Applicable to arrangements with only ordinary multiple points

Enhances understanding of singularity invariants in algebraic geometry

Abstract

The Hodge spectrum is an important analytic invariant of singularities encoding the Hodge filtration and the monodromy of the Milnor fiber. Explicit formulas exist for only a few cases. In this article the main result is a combinatorial formula for homogeneous polynomials in three variables whose reduced one define projective curve arrangements having only ordinary multiple points.