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.
Reihe
Sprache
Verlagsort
Verlagsgruppe
Zielgruppe
Für Beruf und Forschung
Professional
Illustrationen
6 s/w Abbildungen, 7 s/w Tabellen
7 Tables, black and white; 6 Illustrations, black and white
Maße
Höhe: 234 mm
Breite: 156 mm
Dicke: 16 mm
Gewicht
ISBN-13
978-1-58488-860-4 (9781584888604)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Irena Peeva is a professor of mathematics at Cornell University.
Herausgeber*in
Cornell University, Ithaca, New York
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.
