Hyperplane arrangements : an introduction / Alexandru Dimca.
2017
QA169
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Details
Title
Hyperplane arrangements : an introduction / Alexandru Dimca.
Author
Dimca, Alexandru.
ISBN
9783319562216 (electronic book)
3319562215 (electronic book)
9783319562209
3319562207
3319562215 (electronic book)
9783319562209
3319562207
Published
Cham : Springer, 2017.
Language
English
Description
1 online resource.
Item Number
10.1007/978-3-319-56221-6 doi
Call Number
QA169
Dewey Decimal Classification
514/.23
Summary
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.
Bibliography, etc. Note
Includes bibliographical references and index.
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Access limited to authorized users.
Digital File Characteristics
text file PDF
Added Author
Dimca, Alexandru
Series
Universitext.
Available in Other Form
Print version: 3319562207
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Table of Contents
Invitation to the Trip
Hyperplane Arrangements and their Combinatorics
Orlik–Solomon Algebras and de Rham Cohomology
On the Topology of the Complement M(A)
Milnor Fibers and Local Systems
Characteristic Varieties and Resonance Varieties
Logarithmic Connections and Mixed Hodge Structures
Free Arrangements and de Rham Cohomology of Milnor Fibers.
Hyperplane Arrangements and their Combinatorics
Orlik–Solomon Algebras and de Rham Cohomology
On the Topology of the Complement M(A)
Milnor Fibers and Local Systems
Characteristic Varieties and Resonance Varieties
Logarithmic Connections and Mixed Hodge Structures
Free Arrangements and de Rham Cohomology of Milnor Fibers.