Arithmetic of Blowup Algebras

Erscheinungsjahr 2006
ISBN: 978-0-521-45484-1
Verlag: Cambridge University Press

Buch, Englisch, Band 195, 340 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 553 g

Reihe: London Mathematical Society Lecture Note Series

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.

Autoren/Hrsg.

Vasconcelos, Wolmer V.

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Homologische Algebra

Inhaltsverzeichnis

1. Krull dimension; 2. Syzygetic sequences; 3. Approximation complexes; 4. Linkage and Koszul homology; 5. Arithmetic of Rees algebras; 6. Factoriality; 7. Ideal transforms; 8. The equations of Rees algebras; 9. Commuting varieties of algebras; 10. Computational methods in commutative algebra.