Overview
- Provides a clear and rapid introduction to many hot topics in the field of hyperplane arrangements
- Introduces basic definitions and key notions and takes the reader right up to open questions
- Contains a wealth of exercises of varying levels of difficulty
Part of the book series: Universitext (UTX)
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Table of contents (8 chapters)
Keywords
- hyperplane arrangements
- Milnor fibers of arrangements
- topology of arrangement complements
- fundamental groups
- free arrangements and free curves
- Hodge theory of arrangements
- resonance varieties of arrangements
- characteristic varieties of arrangements
- de Rham cohomology of arrangements
- Aomoto complexes
- Orlik-Solomon algebras of arrangements
- MSC (2010): 32S22, 32S55, 32S35, 14F35, 14F40, 14F45, 52C35
- combinatorics
About this book
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.
Reviews
“In the book under review, the author provides an interesting introduction to the theory of hyperplane arrangements. … It is worth pointing out that the text is accessible even for advanced undergraduate students (especially the first three chapters) and motivating since the book focuses on current research problems and provides some open problems. … this is a very nice introduction to the subject.” (Piotr Pokora, zbMATH 1362.14001, 2017)
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Hyperplane Arrangements
Book Subtitle: An Introduction
Authors: Alexandru Dimca
Series Title: Universitext
DOI: https://doi.org/10.1007/978-3-319-56221-6
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG 2017
Softcover ISBN: 978-3-319-56220-9Published: 07 April 2017
eBook ISBN: 978-3-319-56221-6Published: 28 March 2017
Series ISSN: 0172-5939
Series E-ISSN: 2191-6675
Edition Number: 1
Number of Pages: XII, 200
Number of Illustrations: 1 b/w illustrations, 17 illustrations in colour
Topics: Algebraic Geometry, Commutative Rings and Algebras, Several Complex Variables and Analytic Spaces, Algorithms, Projective Geometry, Combinatorics