Syzygies and Hilbert Functions

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Irena Peeva (Cornell University, Ithaca, New York) Zuhair Nashed (University of Central Florida, Orlando, USA)

Syzygies and Hilbert Functions

Irena Peeva (Cornell University, Ithaca, New York), Zuhair Nashed (University of Central Florida, Orlando, USA), Earl Taft , Marc Chardin (Universite Pierre et Marie Curie, Paris, France)

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English

Chapman & Hall/CRC
20 March 2007

Functional analysis & transforms

Series: Lecture Notes in Pure and Applied Mathematics

Hilbert functions and resolutions are both central objects in commutative algebra and fruitful tools in the fields of algebraic geometry, combinatorics, commutative algebra, and computational algebra. Spurred by recent research in this area, Syzygies and Hilbert Functions explores fresh developments in the field as well as fundamental concepts.

Written by international mathematics authorities, the book first examines the invariant of Castelnuovo-Mumford regularity, blowup algebras, and bigraded rings. It then outlines the current status of two challenging conjectures: the lex-plus-power (LPP) conjecture and the multiplicity conjecture. After reviewing results of the geometry of Hilbert functions, the book considers minimal free resolutions of integral subschemes and of equidimensional Cohen-Macaulay subschemes of small degree. It also discusses relations to subspace arrangements and the properties of the infinite graded minimal free resolution of the ground field over a projective toric ring. The volume closes with an introduction to multigraded Hilbert functions, mixed multiplicities, and joint reductions.

By surveying exciting topics of vibrant current research, Syzygies and Hilbert Functions stimulates further study in this hot area of mathematical activity.

Contributions by: Marc Chardin (Universite Pierre et Marie Curie Paris France)
Edited by: Irena Peeva (Cornell University Ithaca New York)
Series edited by: Zuhair Nashed (University of Central Florida Orlando USA), Earl Taft, Earl Taft
Imprint: Chapman & Hall/CRC
Country of Publication: United States
Dimensions: Height: 234mm, Width: 156mm, Spine: 16mm
Weight: 430g
ISBN: 9781584888604
ISBN 10: 1584888601
Series: Lecture Notes in Pure and Applied Mathematics
Pages: 304
Publication Date: 20 March 2007
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

Introduction. Some Results and Questions on Castelnuovo-Mumford Regularity. Hilbert Coefficients of Ideals With a View Toward Blowup Algebra. A Case Study in Bigraded Commutative Algebra. Lex-plus-powers Ideals. Multiplicity Conjectures. The Geometry of Hilbert Functions. Resolutions of Subschemes of Small Degree. Koszul Toric Rings. Resolutions and Subspace Arrangements. Multi-graded Hilbert Functions, Mixed Multiplicities.

Irena Peeva is a professor of mathematics at Cornell University.