Hilbert functions over toric rings

DOI10.1307/mmj/1220879413zbMath1183.13031OpenAlexW1983449574MaRDI QIDQ841539

Noam Horwitz, Irena Peeva, Vesselin N. Gasharov

Publication date: 17 September 2009

Published in: Michigan Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1307/mmj/1220879413

zbMATH Keywords

Hilbert functionBetti numberslex idealsMacaulay's theoremtoric rings

Mathematics Subject Classification ID

Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes (13F55)

Related Items (11)

Hilbert schemes and Betti numbers over Clements–Lindström rings ⋮ Open problems on syzygies and Hilbert functions ⋮ Poset embeddings of Hilbert functions ⋮ Distractions of Shakin rings ⋮ Hilbert schemes and maximal Betti numbers over Veronese rings ⋮ Macaulay's theorem for some projective monomial curves ⋮ Poset embeddings of Hilbert functions for two hypersurface rings ⋮ Toward free resolutions over scrolls ⋮ Toward a theory of monomial preorders ⋮ Rees algebras of square-free monomial ideals ⋮ FFRT properties of hypersurfaces and their F-signatures

Uses Software

• Macaulay2

Cites Work

• Hilbert schemes and maximal Betti numbers over Veronese rings
• Deformation classes of graded modules and maximal Betti numbers
• Squarefree lexsegment ideals
• Unimodular Hermitian and skew-Hermitian forms
• Semigroup rings and simplicial complexes
• Resolutions of \textbf{a}-stable ideals.
• Rationality for generic toric rings
• Hilbert functions and lex ideals
• Flips and the Hilbert scheme over an exterior algebra
• Ideals containing the squares of the variables
• Connectedness of Hilbert scheme
• A toric ring with irrational Poincaré-Betti series
• Connectedness of Hilbert schemes
• Resolutions of monomial ideals and cohomology over exterior algebras
• Upper bounds for the betti numbers of a given hilbert function
• Maximum betti numbers of homogeneous ideals with a given hilbert function
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