Hyperplane Arrangements: Computations and Conjectures

TL;DR

This paper surveys key results and open problems in hyperplane arrangements, emphasizing computational methods, algebraic tools, and connections to other mathematical areas, illustrated with concrete examples and calculations.

Contribution

It provides an overview of computational techniques, algebraic tools, and open problems in hyperplane arrangements, highlighting their connections to various mathematical theories.

Findings

Introduction to essential tools like Koszul and Lie algebra methods

Concrete calculations illustrating theoretical concepts

Discussion of connections to other mathematical areas

Abstract

This paper provides an overview of selected results and open problems in the theory of hyperplane arrangements, with an emphasis on computations and examples. We give an introduction to many of the essential tools used in the area, such as Koszul and Lie algebra methods, homological techniques, and the Bernstein-Gelfand-Gelfand correspondence, all illustrated with concrete calculations. We also explore connections of arrangements to other areas, such as De Concini-Procesi wonderful models, the Feichtner-Yuzvinsky algebra of an atomic lattice, fatpoints and blowups of projective space, and plane curve singularities.