ABSTRACT

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 pro

part I|1 pages

Preliminaries

chapter 1|5 pages

Kronecker Extensions

chapter 2|7 pages

Modules and Kronecker Extensions

chapter 3|10 pages

Numerical Monoids

chapter 4|13 pages

Relations of Numerical Monoids

chapter 5|5 pages

Splitting of Numerical Monoids

part II|1 pages

Regular Sequences

chapter 7|7 pages

Graded Complete Intersections

chapter 8|15 pages

Generic Regular Sequences

part III|1 pages

Elimination

chapter 10|4 pages

Basics of Elimination

chapter 11|11 pages

The Main Case for Generic Regular Sequences

chapter 12|9 pages

The Main Case for Regular Sequences

part IV|1 pages

Resultants

chapter 13|4 pages

Resultant Ideals

chapter 14|10 pages

Resultant Divisors and Duality

chapter 15|10 pages

Resultants

chapter 16|8 pages

Formulas on Resultants