Arithmetic of Blowup Algebras / Wolmer V. Vasconcelos.

By: Vasconcelos, Wolmer V [author.]Material type: TextTextSeries: London Mathematical Society Lecture Note Series ; no. 195Publisher: Cambridge : Cambridge University Press, 1994Description: 1 online resource (340 pages) : digital, PDF file(s)Content type: text Media type: computer Carrier type: online resourceISBN: 9780511574726 (ebook)Subject(s): Commutative algebraAdditional physical formats: Print version: : No titleDDC classification: 512/.24 LOC classification: QA251.3 | .V36 1994Online resources: Click here to access online Summary: This book provides an introduction to recent developments in the theory of blow up algebras - Rees algebras, associated graded rings, Hilbert functions, and birational morphisms. The emphasis is on deriving properties of rings from their specifications in terms of generators and relations. While this limits the generality of many results, it opens the way for the application of computational methods. A highlight of the book is the chapter on advanced computational methods in algebra using Gröbner basis theory and advanced commutative algebra. The author presents the Gröbner basis algorithm and shows how it can be used to resolve computational questions in algebra. This volume is intended for advanced students in commutative algebra, algebraic geometry and computational algebra, and homological algebra. It can be used as a reference for the theory of Rees algebras and related topics.
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This book provides an introduction to recent developments in the theory of blow up algebras - Rees algebras, associated graded rings, Hilbert functions, and birational morphisms. The emphasis is on deriving properties of rings from their specifications in terms of generators and relations. While this limits the generality of many results, it opens the way for the application of computational methods. A highlight of the book is the chapter on advanced computational methods in algebra using Gröbner basis theory and advanced commutative algebra. The author presents the Gröbner basis algorithm and shows how it can be used to resolve computational questions in algebra. This volume is intended for advanced students in commutative algebra, algebraic geometry and computational algebra, and homological algebra. It can be used as a reference for the theory of Rees algebras and related topics.

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