Invitation to the Trip

Abstract

This chapter is a quick introduction, in which we point out the interplay between combinatorics, topology, geometry and arithmetic in the realm of real and complex hyperplane arrangements. After giving some basic definitions, most of the results are stated in the plane, where the reader’s intuition can be strongly supported by drawings. Each of the themes introduced in this chapter is fully developed in a later chapter. We include a discussion of the Sylvester–Gallai property for real line arrangements, both the classical projective version and a new affine version. The proof of both results is inspired by Hirzebruch’s approach. The main topic of this book, the study of the monodromy of the Milnor fiber of a hyperplane arrangement, is also introduced in a very simple setting.