Reduced arithmetically Gorenstein schemes and simplicial polytopes with maximal Betti numbers.
type: Item
instance of: scholarly article
title: Reduced arithmetically Gorenstein schemes and simplicial polytopes with maximal Betti numbers.
zbMATH Open document ID: 1053.13006
DOI: 10.1016/S0001-8708(02)00079-8
author: Uwe Nagel
author: Juan C. Migliore
published in: Advances in Mathematics
publication date: 2004-01-06T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/0103197
review text: An SI-sequence is a finite sequence of positive integers which is symmetric, unimodal and satisfies a growth condition. From an arbitrary SI-sequence the authors construct a reduced, arithmetically Gorenstein configuration of linear varieties, \(G\), of arbitrary dimension whose Artinian reduction has the given SI-sequence as Hilbert function and has the weak Lefschetz property. It is shown that \(G\) has maximal graded Betti numbers among all arithmetically Gorenstein subschemes of the projective space whose Artinian reduction has the weak Lefschetz property and the given Hilbert function. Finally, it is shown that over a field of characteristic zero every set of simplicial polytopes with fixed \(h\)-vector contains a polytope with maximal graded Betti numbers.
Mathematics Subject Classification ID: 13D40
Mathematics Subject Classification ID: 13C40
Mathematics Subject Classification ID: 13D02
Mathematics Subject Classification ID: 14M05
Mathematics Subject Classification ID: 14M06
Mathematics Subject Classification ID: 14N20
Mathematics Subject Classification ID: 13H10
Mathematics Subject Classification ID: 52B12
Mathematics Subject Classification ID: 52B11
zbMATH DE Number: 2022080
zbMATH Keywords: SI-sequence
zbMATH Keywords: Hilbert function
zbMATH Keywords: weak Lefschetz property
zbMATH Keywords: Gorenstein ideal
zbMATH Keywords: graded Betti numbers
zbMATH Keywords: simplicial polytopes
zbMATH Keywords: Gorenstein liaison
zbMATH Keywords: arithmetically Gorenstein subscheme
zbMATH Keywords: compressed algebra
zbMATH Keywords: Gorenstein configuration of linear varieties
reviewed by: Cristodor-Paul Ionescu
describes a project that uses: Macaulay2
MaRDI profile type: Publication
arXiv ID: math/0103197
cites work: Curves of maximum genus in range A and stick-figures
cites work: Upper bounds for the betti numbers of a given hilbert function
cites work: Sufficiency of McMullen’s conditions for 𝑓-vectors of simplicial polytopes
cites work: A proof of the sufficiency of McMullen's conditions for f-vectors of simplicial convex polytopes
cites work: The number of faces of balanced Cohen-Macaulay complexes and a generalized Macaulay theorem
cites work: Gorenstein Artin Algebras and Points in Projective Space
cites work: Betti numbers of compressed level algebras
cites work: The Structure of an Even Liaison Class
cites work: Q3031096
cites work: Q3843140
cites work: Algebra Structures for Finite Free Resolutions, and Some Structure Theorems for Ideals of Codimension 3
cites work: Gorenstein Algebras and the Cayley-Bacharach Theorem
cites work: Irreducibility and dimension theorems for families of height 3 Gorenstein algebras
cites work: Linear free resolutions and minimal multiplicity
cites work: Minimal resolutions of some monomial ideals
cites work: Q3222956
cites work: Monomial ideals and points in projective space
cites work: Extremal point sets and Gorenstein ideals
cites work: An alternative to the Hilbert function for the ideal of a finite set of points in \(\mathbb P^n\)
cites work: The hilbert function and the minimal free resolution of some gorenstein ideals of codimension 4
cites work: Cayley-Bacharach Schemes and Their Canonical Modules
cites work: The Hilbert Function of a Reduced K -Algebra
cites work: A generalized liaison addition
cites work: Reduced Gorenstein codimension three subschemes of projective space
cites work: Smooth points of \(\text{Gor}(T)\)
cites work: \(k\)-configurations in \(\mathbb{P}^3\) all have extremal resolutions
cites work: Some examples of unimodal Gorenstein sequences
cites work: Characterization of Hilbert Functions of Gorenstein Artin Algebras with the Weak Stanley Property
cites work: Connectedness of Hilbert scheme
cites work: Families of curves in 𝑃³ and Zeuthen’s problem
cites work: Q4263563
cites work: Q5288967
cites work: Computation of Betti numbers of monomial ideals associated with stacked polytopes
cites work: Maximum betti numbers of homogeneous ideals with a given hilbert function
cites work: Compressed Algebras: Artin Algebras Having Given Socle Degrees and Maximal Length
cites work: Power sums, Gorenstein algebras, and determinantal loci. With an appendix `The Gotzmann theorems and the Hilbert scheme' by Anthony Iarrobino and Steven L. Kleiman
cites work: Q4885654
cites work: Q4309961
cites work: Gorenstein liaison, complete intersection liaison invariants and unobstructedness
cites work: Q3313982
cites work: The numbers of faces of simplicial polytopes
cites work: The maximum numbers of faces of a convex polytope
cites work: Introduction to liaison theory and deficiency modules
cites work: Lifting monomial ideals
cites work: Q4550586

Reduced arithmetically Gorenstein schemes and simplicial polytopes with maximal Betti numbers. (cites work)
cites work: Even liaison classes generated by Gorenstein linkage

Reduced arithmetically Gorenstein schemes and simplicial polytopes with maximal Betti numbers. (cites work)
cites work: Arithmetically Buchsbaum divisors on varieties of minimal degree

Reduced arithmetically Gorenstein schemes and simplicial polytopes with maximal Betti numbers. (cites work)
cites work: Liaison des variétés algébriques. I

Reduced arithmetically Gorenstein schemes and simplicial polytopes with maximal Betti numbers. (cites work)
cites work: Cohen-Macaulay quotients of polynomial rings

Reduced arithmetically Gorenstein schemes and simplicial polytopes with maximal Betti numbers. (cites work)
cites work: Partial intersections and graded Betti numbers

Reduced arithmetically Gorenstein schemes and simplicial polytopes with maximal Betti numbers. (cites work)
cites work: Combinatorics and commutative algebra.

Reduced arithmetically Gorenstein schemes and simplicial polytopes with maximal Betti numbers. (cites work)
cites work: Hilbert functions of graded algebras

Reduced arithmetically Gorenstein schemes and simplicial polytopes with maximal Betti numbers. (cites work)
cites work: The number of faces of a simplicial convex polytope

Reduced arithmetically Gorenstein schemes and simplicial polytopes with maximal Betti numbers. (cites work)
cites work: Q3744270

Reduced arithmetically Gorenstein schemes and simplicial polytopes with maximal Betti numbers. (cites work)
cites work: Q3792779