A note on Artin Gorenstein algebras with Hilbert function \((1,4,k,k,4,1)\)

DOI10.1090/conm/805/16125MaRDI QIDQ6630006

Nancy Abdallah

Publication date: 30 October 2024

zbMATH Keywords

free resolutionsGorenstein algebraArtinian algebraLefschetz property

Mathematics Subject Classification ID

Commutative rings defined by monomial ideals; Stanley-Reisner face rings; simplicial complexes (13F55) Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (13D40) Syzygies, resolutions, complexes and commutative rings (13D02) Commutative Artinian rings and modules, finite-dimensional algebras (13E10) Other special types of modules and ideals in commutative rings (13C13)

Cites Work

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• Components of the space parametrizing graded Gorenstein Artin algebras with a given Hilbert function
• Some properties of enumeration in the theory of modular systems.
• Ueber die algebraischen Formen, deren Hesse'sche Determinante identisch verschwindet.
• On higher Hessians and the Lefschetz properties
• The weak and strong Lefschetz properties for Artinian \(K\)-algebras
• When does the Hessian determinant vanish identically? (On Gordan and Noether's proof of Hesse's claim)
• Irreducibility and dimension theorems for families of height 3 Gorenstein algebras
• On the weak Lefschetz property for artinian Gorenstein algebras of codimension three
• Lefschetz elements of Artinian Gorenstein algebras and hessians of homogeneous polynomials
• The Lefschetz properties
• Calabi-Yau threefolds in \(\mathbb{P}^n\) and Gorenstein rings
• Lefschetz properties of some codimension three Artinian Gorenstein algebras
• On the Theory of Gordan-Noether on Homogeneous Forms with Zero Hessian (Improved Version)
• Free resolutions and Lefschetz properties of some Artin Gorenstein rings of codimension four
• A theorem of Gordan and Noether via Gorenstein rings

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