Hyperplane Arrangements

An Introduction

  • Alexandru Dimca

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Alexandru Dimca
    Pages 1-14
  3. Alexandru Dimca
    Pages 85-98
  4. Back Matter
    Pages 187-200

About this book

Introduction

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.

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

Authors and affiliations

  • Alexandru Dimca
    • 1
  1. 1.Université Côte d’AzurNiceFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-56221-6
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-56220-9
  • Online ISBN 978-3-319-56221-6
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • About this book