The structure of the inverse system of Gorenstein k-algebras

Abstract

Macaulay's Inverse System gives an effective method to construct Artinian Gorenstein k-algebras. To date a general structure for Gorenstein k-algebras of any dimension (and codimension) is not understood. In this paper we extend Macaulay's correspondence characterizing the submodules of the divided power ring in one-to-one correspondence with Gorenstein d-dimensional k-algebras. We discuss effective methods for constructing Gorenstein graded rings. Several examples illustrating our results are given.

arXiv comment19 pages, to appear in Advances in Mathematics

References in corpus (4)

• Inverse-syst.lib, Singular library for computing Macaulay's inverse systems
• Inverse Systems of Zero-dimensional Schemes in P^n
• Poincaré series of modules over compressed Gorenstein local rings
• Artinian Gorenstein algebras of embedding dimension four: Components of PGor(H) for H=(1,4,7,..., 1)

Cited by in corpus (6)

• Symmetric Decomposition of the Associated Graded Algebra of an Artinian Gorenstein Algebra
• Inverse limits of Macaulay's inverse systems
• Gorenstein algebras and toric bundles
• A constructive approach to one-dimensional Gorenstein $k$-algebras
• Almost finitely generated inverse systems and reduced k-algebras
• VSPs of cubic fourfolds and the Gorenstein locus of the Hilbert scheme of 14 points on A^6