Author | Orlik, Peter. author |
---|---|

Title | Arrangements of Hyperplanes [electronic resource] / by Peter Orlik, Hiroaki Terao |

Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1992 |

Connect to | http://dx.doi.org/10.1007/978-3-662-02772-1 |

Descript | XVIII, 325 p. online resource |

SUMMARY

An arrangement of hyperplanes is a finite collection of codimension one affine subspaces in a finite dimensional vector space. Arrangements have emerged independently as important objects in various fields of mathematics such as combinatorics, braids, configuration spaces, representation theory, reflection groups, singularity theory, and in computer 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. It emphasizes general techniques which illuminate the connections among the different aspects of the subject. Its main purpose is to lay the foundations of the theory. Consequently, it is essentially self-contained and proofs are provided. Nevertheless, there are several new results here. In particular, many theorems that were previously known only for central arrangements are proved here for the first time in completegenerality. The text provides the advanced graduate student entry into a vital and active area of research. The working mathematician will findthe book useful as a source of basic results of the theory, open problems, and a comprehensive bibliography of the subject

CONTENT

1. Introduction -- 2. Combinatorics -- 3. Algebras -- 4. Free Arrangements -- 5. Topology -- 6. Reflection Arrangements -- A. Some Commutative Algebra -- B. Basic Derivations -- C. Orbit Types -- D. Three-Dimensional Restrictions -- References -- Index of Symbols

Mathematics
Algebraic geometry
Functions of complex variables
Algebraic topology
Manifolds (Mathematics)
Complex manifolds
Mathematics
Algebraic Topology
Algebraic Geometry
Manifolds and Cell Complexes (incl. Diff.Topology)
Several Complex Variables and Analytic Spaces