The resolution of the bracket powers of the maximal ideal in a diagonal hypersurface ring

DOI10.1016/j.jalgebra.2012.07.011zbMath1275.13003arXiv1012.1026OpenAlexW2962738653MaRDI QIDQ1946109

Hamidreza Rahmati, Andrew R. Kustin, Adela Vraciu

Publication date: 17 April 2013

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1012.1026

zbMATH Keywords

syzygyPfaffiansweak Lefschetz propertyFrobenius periodicityHilbert-Burch matrixsyzygy gapalmost complete intersectionFrobenius powerenumeration of plane partitionsHilbert-Kunz functionssocle degrees

Mathematics Subject Classification ID

Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13H10) Linkage, complete intersections and determinantal ideals (13C40) Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (13D40) Syzygies, resolutions, complexes and commutative rings (13D02) Characteristic (p) methods (Frobenius endomorphism) and reduction to characteristic (p); tight closure (13A35) Commutative Artinian rings and modules, finite-dimensional algebras (13E10)

Related Items (12)

Rank-2 syzygy bundles on Fermat curves and an application to Hilbert-Kunz functions ⋮ Socle degrees, resolutions, and Frobenius powers ⋮ The weak Lefschetz property for monomial ideals of small type ⋮ An explicit example of Frobenius periodicity ⋮ The Weak Lefschetz Property for monomial complete intersection in positive characteristic ⋮ Use DG-methods to build a matrix factorization ⋮ Asymptotic behavior of the socle of Frobenius powers ⋮ Squeezed complexes ⋮ Syzygy bundles and the weak Lefschetz property of monomial almost complete intersections ⋮ The resolution of \((x^N,y^N,z^N,w^N)\) ⋮ On the weak Lefschetz property for artinian Gorenstein algebras of codimension three ⋮ The syzygies of the ideal \((x_1^N, x_2^N, x_3^N, x_4^N)\) in the hypersurface ring defined by \(x_1^n + x_2^n + x_3^n + x_4^n\)

Cites Work

• Unnamed Item
• Monomial complete intersections, the weak Lefschetz property and plane partitions
• Dimension projective finie et cohomologie locale. Applications à la demonstration de conjectures de M. Auslander, H. Bass et A. Grothendieck
• Socle degrees, resolutions, and Frobenius powers
• On the structure of free resolutions of length 3
• Poincaré series of modules over local rings of small embedding codepth or small linking number
• Some surprising Hilbert-Kunz functions
• A cohomological study of local rings of embedding codepth 3
• An explicit example of Frobenius periodicity
• Socle degrees of Frobenius powers
• A note on the weak Lefschetz property of monomial complete intersections in positive characteristic
• Mason's theorem and syzygy gaps
• The Weak Lefschetz Property for monomial complete intersection in positive characteristic
• F-Purity and Rational Singularity
• Algebra Structures for Finite Free Resolutions, and Some Structure Theorems for Ideals of Codimension 3

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