  Arrangements of hyperplanes

Peter Orlik, Hiroaki Terao

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.

「Nielsen BookData」より

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.

「Nielsen BookData」より

[目次]

• 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.

「Nielsen BookData」より

[目次]

• 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.

「Nielsen BookData」より 書名 Arrangements of hyperplanes Orlik, Peter 寺尾 宏明 Terao Hiroaki Die Grundlehren der mathematischen Wissenschaften Springer-Verlag c1992 1st ed. Softcover of orig. ed. 1992 xviii, 325 p. 24 cm 0387552596 3540552596 9783642081378 BA18303017 ※クリックでCiNii Booksを表示 英語 ドイツ    