Arrangements Of Hyperplanes
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Arrangements Of Hyperplanes
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Author : Peter Orlik
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Arrangements Of Hyperplanes written by Peter Orlik and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
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.
Arrangements Of Hyperplanes
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Author : Peter Orlik (mathématicien.)
language : en
Publisher:
Release Date : 1991
Arrangements Of Hyperplanes written by Peter Orlik (mathématicien.) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with categories.
Arrangements Of Hyperplanes
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Author : Peter Orlik
language : en
Publisher:
Release Date : 2014-01-15
Arrangements Of Hyperplanes written by Peter Orlik and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Facing Up To Arrangements Face Count Formulas For Partitions Of Space By Hyperplanes
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Author : Thomas Zaslavsky
language : en
Publisher: American Mathematical Soc.
Release Date : 1975
Facing Up To Arrangements Face Count Formulas For Partitions Of Space By Hyperplanes written by Thomas Zaslavsky and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with Mathematics categories.
An arrangement of hyperplanes of Euclidean or projective d-space is a finite set of hyperplanes, together with the induced partition of the space. Given the hyperplanes of an arrangement, how can the faces of the induced partition be counted? Heretofore this question has been answered for the plane, Euclidean 3-space, hyperplanes in general position, and the d-faces of the hyperplanes through the origin in Euclidean space. In each case the numbers of k-faces depend only on the incidences between intersections of the hyperplane, even though arrangements with the same intersection incidence pattern are not in general combinatorially isomorphic. We generalize this fact by demonstrating formulas for the numbers of k-faces of all Euclidean and projective arrangements, and the numbers of bounded k-faces of the former, as functions of the (semi)lattice of intersections of the hyperplanes, not dependent on the arrangement's combinatorial type.
On Logarithmic Forms And Arrangements Of Hyperplanes
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Author : Ki-sŏk Yi
language : en
Publisher:
Release Date : 1995
On Logarithmic Forms And Arrangements Of Hyperplanes written by Ki-sŏk Yi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with categories.
Geometry And Topology Of Hyperplane Arrangements
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Author : Michael J. Falk
language : en
Publisher:
Release Date : 1983
Geometry And Topology Of Hyperplane Arrangements written by Michael J. Falk and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Hyperplanes categories.
Hyperplane Arrangements
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Author : Alexandru Dimca
language : en
Publisher: Springer
Release Date : 2017-03-28
Hyperplane Arrangements written by Alexandru Dimca and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-03-28 with Mathematics categories.
This textbook provides an accessible introduction to the rich and beautiful area of hyperplane arrangement theory, where discrete mathematics, in the form of combinatorics and arithmetic, meets continuous mathematics, in the form of the topology and Hodge theory of complex algebraic varieties. The topics discussed in this book range from elementary combinatorics and discrete geometry to more advanced material on mixed Hodge structures, logarithmic connections and Milnor fibrations. The author covers a lot of ground in a relatively short amount of space, with a focus on defining concepts carefully and giving proofs of theorems in detail where needed. Including a number of surprising results and tantalizing open problems, this timely book also serves to acquaint the reader with the rapidly expanding literature on the subject. Hyperplane Arrangements will be particularly useful to graduate students and researchers who are interested in algebraic geometry or algebraic topology. The book contains numerous exercises at the end of each chapter, making it suitable for courses as well as self-study.
Introduction To Arrangements
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Author : Peter Orlik
language : en
Publisher: American Mathematical Soc.
Release Date : 1989
Introduction To Arrangements written by Peter Orlik and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.
Topics In Hyperplane Arrangements Polytopes And Box Splines
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Author : Corrado De Concini
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-08-30
Topics In Hyperplane Arrangements Polytopes And Box Splines written by Corrado De Concini and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-08-30 with Mathematics categories.
Topics in Hyperplane Arrangements, Polytopes and Box-Splines brings together many areas of research that focus on methods to compute the number of integral points in suitable families or variable polytopes. The topics introduced expand upon differential and difference equations, approximation theory, cohomology, and module theory. This book, written by two distinguished authors, engages a broad audience by proving the a strong foudation. This book may be used in the classroom setting as well as a reference for researchers.
Topics In Hyperplane Arrangements
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Author : Marcelo Aguiar
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-11-22
Topics In Hyperplane Arrangements written by Marcelo Aguiar and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-22 with Mathematics categories.
This monograph studies the interplay between various algebraic, geometric and combinatorial aspects of real hyperplane arrangements. It provides a careful, organized and unified treatment of several recent developments in the field, and brings forth many new ideas and results. It has two parts, each divided into eight chapters, and five appendices with background material. Part I gives a detailed discussion on faces, flats, chambers, cones, gallery intervals, lunes and other geometric notions associated with arrangements. The Tits monoid plays a central role. Another important object is the category of lunes which generalizes the classical associative operad. Also discussed are the descent and lune identities, distance functions on chambers, and the combinatorics of the braid arrangement and related examples. Part II studies the structure and representation theory of the Tits algebra of an arrangement. It gives a detailed analysis of idempotents and Peirce decompositions, and connects them to the classical theory of Eulerian idempotents. It introduces the space of Lie elements of an arrangement which generalizes the classical Lie operad. This space is the last nonzero power of the radical of the Tits algebra. It is also the socle of the left ideal of chambers and of the right ideal of Zie elements. Zie elements generalize the classical Lie idempotents. They include Dynkin elements associated to generic half-spaces which generalize the classical Dynkin idempotent. Another important object is the lune-incidence algebra which marks the beginning of noncommutative Möbius theory. These ideas are also brought upon the study of the Solomon descent algebra. The monograph is written with clarity and in sufficient detail to make it accessible to graduate students. It can also serve as a useful reference to experts.