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Regular sequences and resultants

Author: Günter Scheja; Uwe Storch
Publisher: Natick, Mass. : A K Peters, ©2001.
Series: Research notes in mathematics (Boston, Mass.), 8.
Edition/Format:   eBook : Document : EnglishView all editions and formats
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
(DLC) 2001022483
(OCoLC)46401634
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Günter Scheja; Uwe Storch
ISBN: 9781439863657 1439863652
OCLC Number: 1029336949
Description: 1 online resource.
Contents: 1Kronecker Extensions1 --
2Modules and Kronecker Extensions6 --
3Numerical Monoids13 --
4Relations of Numerical Monoids23 --
5Splitting of Numerical Monoids36 --
IIRegular Sequences --
6Regular Sequences and Complete Intersections41 --
7Graded Complete Intersections53 --
8Generic Regular Sequences60 --
9Generic Structure of the Principal Component75 --
IIIElimination --
10Basics of Elimination81 --
11Main Case for Generic Regular Sequences85 --
12Main Case for Regular Sequences96 --
IVResultants --
13Resultant Ideals105 --
14Resultant Divisors and Duality109 --
15Resultants119 --
16Formulas on Resultants129.
Series Title: Research notes in mathematics (Boston, Mass.), 8.
Responsibility: Günter Scheja, Uwe Storch.

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 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.

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