Syzygies and Hilbert Functions (Paperback) (ISBN-13: 9781584888604)

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.

Author: Irena Peeva
ISBN-10: 1584888601
ISBN-13: 9781584888604
Publisher: CRC Press
Language: English
Published: 03/20/2007
Pages: 304
Format: Paperback
Weight: 0.96lbs
Size: 9.12h x 6.37w x 0.66d

Review Citation(s):
Scitech Book News 06/01/2007 pg. 24