Arrangements of Hyperplanes

An arrangement of hyperplanes is a finite collection ofcodimension one affine subspaces in a finite dimensionalvector space. Arrangements have emerged independently asimportant objects in various fields of mathematics such ascombinatorics, braids, configuration spaces, representationtheory, reflection groups, singularity theory, and incomputer science and physics. This book is the first comprehensive study of the subject. It treats arrangements with methods from combinatorics,algebra, algebraic geometry, topology, and group actions. Itemphasizes general techniques which illuminate theconnections among the different aspects of the subject. Itsmain purpose is to lay the foundations of the theory. Consequently, it is essentially self-contained and proofsare provided. Nevertheless, there are several new resultshere. In particular, many theorems that were previouslyknown only for central arrangements are proved here for thefirst time in completegenerality. The text provides the advanced graduate student entry into avital and active area of research. The working mathematicianwill findthe book useful as a source of basic results ofthe theory, open problems, and a comprehensive bibliographyof the subject.

An arrangement of hyperplanes is a finite collection ofcodimension one affine subspaces in a finite dimensionalvector space. Arrangements have emerged independently asimportant objects in various fields of mathematics such ascombinatorics, braids, configuration spaces, representationtheory, reflection groups, singularity theory, and incomputer science and physics. This book is the first comprehensive study of the subject. It treats arrangements with methods from combinatorics,algebra, algebraic geometry, topology, and group actions. Itemphasizes general techniques which illuminate theconnections among the different aspects of the subject. Itsmain purpose is to lay the foundations of the theory. Consequently, it is essentially self-contained and proofsare provided. Nevertheless, there are several new resultshere. In particular, many theorems that were previouslyknown only for central arrangements are proved here for thefirst time in completegenerality. The text provides the advanced graduate student entry into avital and active area of research. The working mathematicianwill findthe book useful as a source of basic results ofthe theory, open problems, and a comprehensive bibliographyof the subject.