Arithmetic of Blowup Algebras

This book discusses recent developments in an important area of computational commutative algebra.

Wolmer V. Vasconcelos (Author)

9780521454841, Cambridge University Press

Paperback, published 25 February 1994

340 pages
22.9 x 15.2 x 1.8 cm, 0.483 kg

'…an interesting collection of facts not easily found elsewhere.' Mathematika

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.

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.

Subject Areas: Algebra [PBF]