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Hyperplane arrangements : an introduction / Alexandru Dimca.

By: Dimca, Alexandru [author].
Material type: TextTextSeries: Universitext.Publisher: Cham : Springer, 2017Description: xii, 200 pages : illustrations (some color) ; 24 cm.ISBN: 9783319562209.Subject(s): Cohomology operations | Combinatorial analysisDDC classification: 514.23
Contents:
1. Invitation to the Trip -- 2. Hyperplane Arrangements and their Combinatorics -- 3. Orlik--Solomon Algebras and de Rham Cohomology -- 4. On the Topology of the Complement M(A) -- 5. Milnor Fibers and Local Systems -- 6. Characteristic Varieties and Resonance Varieties -- 7. Logarithmic Connections and Mixed Hodge Structures -- 8. Free Arrangements and de Rham Cohomology of Milnor Fibers.
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.
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Item type Current location Call number Status Date due Barcode Item holds
Books Books ISI Library, Kolkata
 
514.23 D582 (Browse shelf) Available 138292
Total holds: 0

includes bibliographical references and index.

1. Invitation to the Trip --
2. Hyperplane Arrangements and their Combinatorics --
3. Orlik--Solomon Algebras and de Rham Cohomology --
4. On the Topology of the Complement M(A) --
5. Milnor Fibers and Local Systems --
6. Characteristic Varieties and Resonance Varieties --
7. Logarithmic Connections and Mixed Hodge Structures --
8. Free Arrangements and de Rham Cohomology of Milnor Fibers.

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.

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