Arithmetic of Blowup Algebras [Paperback]

This book discusses recent developments in an important area of computational commutative algebra.The theory of blowup algebras--Rees algebras, associated graded rings, Hilbert functions, and birational morphisms--is undergoing a period of rapid development. This book provides an introduction for advanced students in commutative algebra, algebraic geometry and computational and homological algebra.The theory of blowup algebras--Rees algebras, associated graded rings, Hilbert functions, and birational morphisms--is undergoing a period of rapid development. This book provides an introduction for advanced students in commutative algebra, algebraic geometry and computational and homological algebra.The theory of blowup algebras--Rees algebras, associated graded rings, Hilbert functions, and birational morphisms--is undergoing a period of rapid development. One of the aims of this book is to provide an introduction to these developments. The emphasis is on deriving properties of rings from their specifications in terms of generators and relations. While this places limitations on 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 built on current understanding of Gröbner basis theory and advanced commutative algebra. In a concise way, the author presents the Gröbner basis algorithm and shows how it can be used to resolve many computational questions in algebra.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. In this excellent book the blowup algebras are introduced systematically; many significant results and methods are compiled from recently published work or form work still in pl