A family of ideals with few generators in low degree and large projective dimension

DOI10.1090/S0002-9939-2010-10792-XzbMath1215.13007arXiv1005.3361OpenAlexW2006766469MaRDI QIDQ3005613

Jason McCullough

Publication date: 9 June 2011

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1005.3361

zbMATH Keywords

projective dimensionpolynomial ringhomogeneous ideal

Mathematics Subject Classification ID

Homological dimension and commutative rings (13D05) Syzygies, resolutions, complexes and commutative rings (13D02)

Related Items (10)

Cubics in 10 variables vs. cubics in 1000 variables: Uniformity phenomena for bounded degree polynomials ⋮ The regularity conjecture for prime ideals in polynomial rings ⋮ Syzygies over a polynomial ring ⋮ Multiple structures with arbitrarily large projective dimension supported on linear subspaces ⋮ Strength conditions, small subalgebras, and Stillman bounds in degree ≤4 ⋮ The projective dimension of codimension two algebras presented by quadrics ⋮ A tight bound on the projective dimension of four quadrics ⋮ Ideals with larger projective dimension and regularity ⋮ Three themes of syzygies ⋮ Small subalgebras of polynomial rings and Stillman’s Conjecture

Uses Software

• Macaulay2

Cites Work

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• Open problems on syzygies and Hilbert functions
• A bound on the projective dimension of three cubics
• 'Jede' endliche freie Auflösung ist freie Auflösung eines von drei Elementen erzeugten Ideals
• On the projective dimension and the unmixed part of three cubics
• Some Ideals with Large Projective Dimension
• Ideals Generated by Three Elements

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