Regular Sequences and Resultants

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.

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

Professional Practice & Development

Scheja, Gunter; Storch, Uwe