Determinantal Ideals

by Miro-roig, Rosa M.

• ISBN13: 9783764385347
• ISBN10: 3764385340
• Format: Hardcover
• Copyright: 2008-01-03
• Publisher: Birkhauser

Summary

Determinantal ideals are a central topic in both commutative algebra and algebraic geometry. In this book, three problems are addressed: CI-liaison class and G-liaison class of standard determinantal ideals; the multiplicity conjecture for standard determinantal ideals; unobstructedness and dimension of families of standard determinantal ideals. Winner of the Ferran Sunyer i Balaguer Prize 2007.

Table of Contents

Introduction	p. xi
Background
Minimal free resolutions, ACM schemes, and AG schemes	p. 1
Determinantal ideals	p. 13
CI-liaison and G-liaison	p. 21
CI-liaison and G-liaison of Standard Determinantal Ideals
CI-liaison class of Cohen-Macaulay codimension 2 ideals	p. 30
CI-liaison class of standard determinantal ideals	p. 33
G-liaison class of standard determinantal ideals	p. 41
Multiplicity Conjecture for Standard Determinantal Ideals
The multiplicity conjecture for Cohen-Macaulay codimension 2 ideals	p. 47
The multiplicity conjecture for standard determinantal ideals	p. 50
Unobstructedness and Dimension of Families of Standard Determinantal Ideals
Families of codimension 2 Cohen-Macaulay algebras	p. 65
Unobstructedness and dimension of families of determinantal schemes	p. 67
Determinantal Ideals, Symmetric Determinantal Ideals, and Open Problems
Liaison class of determinantal and symmetric determinantal ideals	p. 106
The multiplicity conjecture for determinantal and symmetric determinantal ideals	p. 111
Unobstructedness and dimension of families of determinantal and symmetric determinantal ideals	p. 119
Bibliography	p. 129
Index	p. 135
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