Spectrum of hyperplane arrangements in four variables

TL;DR

This paper provides a new formula for computing the Hodge spectrum of reduced hyperplane arrangements in four variables, addressing a complex problem in singularity theory.

Contribution

It introduces a formula specifically for reduced hyperplane arrangements in four variables, advancing the understanding of their Hodge spectrum.

Findings

Derived a formula for the Hodge spectrum in four-variable arrangements

Simplified computation of invariants in singularity theory

Extended the class of arrangements with known spectra

Abstract

One of the most important invariants in singularity theory is the Hodge spectrum. Calculating the Hodge spectrum is a difficult task and formulas exist for only a few cases. In this article the main result is the formula for reduced hyperplane arrangements in four variables.