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CRC Press Syzygies and Hilbert Functions: 254 (Lecture Notes in Pure and Applied Mathematics)

Name: Syzygies and Hilbert Functions: 254 (Lecture Notes in Pure and Applied Mathematics)
Brand: CRC Press

Algebra

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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.

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Brand: CRC Press
Format: Paperback
ASIN: 1584888601
Category: Books > Subjects > Science, Nature & Maths > Mathematics > Algebra
Domain: Amazon UK
Release Date: 20 March 2007
Listed Since: 13 February 2007

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CRC Press Syzygies and Hilbert Functions: 254 (Lecture Notes in Pure and Applied Mathematics)

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