Syzygies and Hilbert Functions  book cover
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Syzygies and Hilbert Functions





ISBN 9781584888604
Published March 20, 2007 by Chapman and Hall/CRC
304 Pages - 6 B/W Illustrations

 
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Book Description

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.

Table of Contents

Some Results and Questions on Castelnuovo-Mumford
Regularity
Marc Chardin

Hilbert Coefficients of Ideals with a View toward Blowup Algebras Alberto Corso and Claudia Polini

A Case Study in Bigraded Commutative Algebra
David Cox, Alicia Dickenstein and Hal Schenck

Lex-Plus-Powers Ideals
Christopher A. Francisco and Benjamin P. Richert

Multiplicity Conjectures
Christopher A. Francisco and Hema Srinivasan

The Geometry of Hilbert Functions
Juan C. Migliore

Minimal Free Resolutions of Projective Subschemes of Small Degree
Uwe Nagel

Infinite Free Resolutions over Toric Rings
Irena Peeva

Resolutions and Subspace Arrangements
Jessica Sidman

Multigraded Hilbert Functions and Mixed Multiplicities
Irena Swanson

Index

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