Hyperplane Arrangements

Lecture notes on hyperplane arrangements (114 pages) based on a lecture series at the Park City Mathematics Institute, July 12-19, 2004: pdf file (version of 26 February 2006). These notes provide an introduction to hyperplane arrangements, focusing on connections with combinatorics, at the beginning graduate student level. Background material on posets and matroids is included, as well as numerous exercises. After going through these notes a student should be ready to study the deeper algebraic and topological aspects of the theory of hyperplane arrangements. The notes are published in in Geometric Combinatorics (E. Miller, V. Reiner, and B. Sturmfels, eds.), IAS/Park City Mathematics Series, vol. 13, American Mathematical Society, Providence, RI, 2007, pp. 389-496.

The Notes consist of six lectures with accompanying exercises:

  1. Basic definitions, the intersection poset and the characteristic polynomial
  2. Properties of the intersection poset and graphical arrangements
  3. Matroids and geometric lattices
  4. Broken circuits, modular elements, and supersolvability
  5. Finite fields
  6. Separating hyperplanes

Errata (pdf file), version of 18 October 2020. These errata are for the version published in the Park City Mathematics Series, linked above. Most of them were found by Steven Sam and Darij Grinberg.