Regular Sequences and Resultants / Edition 1

by Gunter Scheja, Uwe Storch

Overview

This carefully prepared manuscript presents elimination theory in weighted projective spaces over arbitrary noetherian commutative base rings. Elimination theory is a classical topic in commutative algebra and algebraic geometry, and it has become of renewed importance recently in the context of applied and computational algebra. This monograph provides a valuable complement to sparse elimination theory in that it presents in careful detail the algebraic difficulties from working over general base rings. This is essential for applications in arithmetic geometry and many other places. Necessary tools concerning monoids of weights, generic polynomials and regular sequences are treated independently in the first part of the book. Many supplements added to each chapter provide extra details and insightful examples. Necessary tools concerning monoids of weights, generic polynomials and regular sequences are treated independently in the first part of the book. Many supplements added to each chapter provide extra details and insightful examples.

Product Details

ISBN-13:	9781568811512
Publisher:	Taylor & Francis
Publication date:	05/18/2001
Series:	Research Notes in Mathematics Series , #8
Pages:	152
Product dimensions:	6.00(w) x 9.00(h) x (d)

About the Author

Scheja, Gunter; Storch, Uwe

Table of Contents

I: Preliminaries 1. Kronecker Extensions 2. Modules and Kronecker Extensions 3. Numerical Monoids 4. Relations of Numerical Monoids 5. Splitting of Numerical Monoids II: Regular Sequences 6. Regular Sequences and Complete Intersections 7. Graded Complete Intersections 8. Generic Regular Sequences 9. The Generic Structure of the Principal Component III: Elimination 10. Basics of Elimination 11. The Main Case for Generic Regular Sequences 12. The Main Case for Regular Sequences IV: Resultants 13. Resultant Ideals 14. Resultant Divisors and Duality 15. Resultants 16. Formulas on Resultants

Editorial Reviews

This research monograph presents elimination theory in weighted projective spaces over arbitrary noetherian commutative base rings. It describes the algebraic difficulties of working over general base rings, which is essential for many applications including arithmetic geometry. In particular, a new approach to the construction and interpretation of resultants and their divisors has been developed using explicit duality for complete intersections. Necessary tools concerning monoids of weights, generic polynomials, and regular sequences are treated independently. Supplements to each section provide extra details and examples. Scheja teaches at Universit<:a>t T<:u>bingen. Storch teaches at Ruhr-Universit<:a>t Bochum. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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