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9781568811512

Regular Sequences and Resultants

by
  • ISBN13:

    9781568811512

  • ISBN10:

    1568811519

  • Format: Hardcover
  • Copyright: 2001-05-18
  • Publisher: A. K. Peters

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Summary

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.

Table of Contents

I Preliminaries
Kronecker Extensions
1(5)
Modules and Kronecker Extensions
6(7)
Numerical Monoids
13(10)
Relations of Numerical Monoids
23(13)
Splitting of Numerical Monoids
36(5)
II Regular Sequences
Regular Sequences and Complete Intersections
41(12)
Graded Complete Intersections
53(7)
Generic Regular Sequences
60(15)
The Generic Structure of the Principal Component
75(6)
III Elimination
Basics of Elimination
81(4)
The Main Case for Generic Regular Sequences
85(11)
The Main Case for Regular Sequences
96(9)
IV Resultants
Resultant Ideals
105(4)
Resultant Divisors and Duality
109(10)
Resultants
119(10)
Formulas on Resultants
129(8)
References 137(4)
Index 141

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