Spectrum of Hyperplane Arrangements in Four Variables

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.

Key Words:

• Hodge spectrum
• Hyperplane arrangement
• Singularity
• Spectrum formula

2010 Mathematics Subject Classification:

• Primary 14B05
• Secondary 32S22

ACKNOWLEDGMENT

The author would like to thank his advisor, Nero Budur, as well as Melissa Davidson and Gabriel C. Drummond-Cole for constructive conversations about this paper and the Department of Mathematics at the University of Notre Dame for supporting him in his doctoral studies. He also thanks Alexandru Dimca for a correction and useful comments.

Notes

Communicated by U. Walther.