advanced computational algebra
algebraic geometry methods
applied mathematics
betti
Betti Diagram
Betti Numbers
bigraded ring analysis
blowup algebra techniques
castelnuovo-mumford regularity
Category=PBD
Category=PBF
Category=PBH
Category=PBKF
Category=PBV
Cohen-Macaulay subschemes
combinatorics
commutative algebra
Complete Intersection Ideal
complex
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
finitely
free
Free Resolution
generated
Generic Initial Ideal
Graded Betti Numbers
Hilbert Coefficients
Hilbert Functions
ideal
koszul
Koszul Complex
Lex Segment Ideal
Macaulay's Theorem
Macaulay’s Theorem
minimal
Minimal Free Graded Resolution
Minimal Free Resolution
minimal free resolution applications
Minimal Generators
Mixed Multiplicities
monomial
Monomial Ideal
multigraded rings
multiplicity conjectures
operator theory
Rational Normal Scrolls
Rees Algebra
resolution
Short Exact Sequence
Stanley Reisner Ideal
subspace arrangement theory
Syzygy Module
Toric Ideal
Toric Ring
Product details
- ISBN 9781584888604
- Weight: 430g
- Dimensions: 156 x 234mm
- Publication Date: 20 Mar 2007
- Publisher: Taylor & Francis Inc
- Publication City/Country: US
- Product Form: Paperback
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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.
Irena Peeva is a professor of mathematics at Cornell University.
