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Hyperplane Arrangements [electronic resource] : An Introduction / by Alexandru Dimca.

By: Dimca, Alexandru [author.].
Contributor(s): SpringerLink (Online service).
Material type: TextTextSeries: Universitext: Publisher: Cham : Springer International Publishing : Imprint: Springer, 2017Description: XII, 200 p. 18 illus., 17 illus. in color. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783319562216.Subject(s): Geometry, algebraic | Algebra | Differential equations, partial | Algorithms | Combinatorics | Algebraic Geometry | Commutative Rings and Algebras | Several Complex Variables and Analytic Spaces | Algorithms | Projective Geometry | CombinatoricsAdditional physical formats: Printed edition:: No title; Printed edition:: No titleDDC classification: 516.35 Online resources: Click here to access online
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.
In: Springer eBooksSummary: 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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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.

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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