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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.

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

Name: Syzygies and Hilbert Functions (Paperback)Chapman and Hall/CRC 
Description: Edited by Irena PeevaSeries Editor: Zuhair Nashed, Earl TaftContributors: Alberto Corso, Marc Chardin, David A. Cox, Juan C. Migliore, Christopher Francisco, Alicia Dickenstein, Uwe Nagel, Claudia Polini, Benjamin P. Richert, Hal Schenck, Jessica Sidman, Hema Srinivasan, Irena Swanson. 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...
Categories: Number Theory, Algebra, Combinatorics