Syzygies and Hilbert FunctionsIrena Peeva 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. |
Contents
Chapter 2 Hilbert Coefficients of Ideals with a View Toward Blowup Algebras | 41 |
Chapter 3 A Case Study in Bigraded Commutative Algebra | 67 |
Chapter 4 LexPlusPowers Ideals | 113 |
Chapter 5 Multiplicity Conjectures | 145 |
Chapter 6 The Geometry of Hilbert Functions | 179 |
Chapter 7 Minimal Free Resolutions of Projective Subschemes of Small Degree | 209 |
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Common terms and phrases
A-regular a₁ Ahn-Migliore Artinian associated graded ring base locus Betti diagram bound of Conjecture Castelnuovo-Mumford regularity characteristic zero codimension Cohen-Macaulay Cohen-Macaulay ring cohomology commutative algebra complete intersection compute d₁ defined depth dimension Eisenbud element Equation Example finite given Hilbert function Gorenstein gr₁(R graded Betti numbers graded free resolution graded ring Gröbner basis Hence Herzog Hilbert coefficients Hilbert function Hilbert scheme homogeneous ideal I₁ initial ideal integer integral closure irreducible Koszul complex Lemma lex ideal lex-plus-powers linear forms LPP ideal m-primary ideal M₁ Macaulay mapping cone Math matrix Migliore minimal free resolution minimal graded free monomial ideals Nagel non-Koszul syzygy nonminimal Peeva polynomial proof Proposition proved R-module reduction number reg(I reg(M regular sequence result Section short exact sequence socle squarefree stable ideal Sturmfels subscheme syzygy syzygy module toric ideal toric ring upper bound zero-dimensional scheme