Jordan types with small parts for Artinian Gorenstein algebras of codimension three

DOI10.1016/j.laa.2022.03.013OpenAlexW3046988724MaRDI QIDQ2134555

Nasrin Altafi

Publication date: 3 May 2022

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2008.02338

zbMATH Keywords

partitionHilbert functionHessiansJordan typeMacaulay dual generatorsArtinian Gorenstein algebracatalecticant matrix

Mathematics Subject Classification ID

Combinatorial aspects of partitions of integers (05A17) Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13H10) Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (13D40) Commutative Artinian rings and modules, finite-dimensional algebras (13E10) Combinatorial aspects of commutative algebra (05E40)

Uses Software

• Macaulay2

Cites Work

• Unnamed Item
• The central simple modules of Artinian Gorenstein algebras
• On higher Hessians and the Lefschetz properties
• Nilpotent matrices having a given Jordan type as maximum commuting nilpotent orbit
• Power sums, Gorenstein algebras, and determinantal loci. With an appendix `The Gotzmann theorems and the Hilbert scheme' by Anthony Iarrobino and Steven L. Kleiman
• The weak and strong Lefschetz properties for Artinian \(K\)-algebras
• On mixed Hessians and the Lefschetz properties
• Complete intersection Jordan types in height two
• Lefschetz elements of Artinian Gorenstein algebras and hessians of homogeneous polynomials
• Free extensions and Jordan type
• The weak Lefschetz property for Artinian Gorenstein algebras of codimension three
• The Jordan type of graded Artinian Gorenstein algebras

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