The explicit minimal resolution constructed from a Macaulay inverse system

TL;DR

This paper provides explicit polynomial formulas for minimal resolutions of Artinian Gorenstein algebras of embedding codimension three, based on their Macaulay inverse systems, advancing the constructive understanding of these algebraic structures.

Contribution

It explicitly constructs minimal resolutions of Artinian Gorenstein algebras of embedding codimension three from Macaulay inverse systems, extending previous existence results.

Findings

Explicit formulas for minimal resolutions derived from inverse systems

Construction applies specifically to codimension three cases

Advances the explicit understanding of Gorenstein algebra resolutions

Abstract

This is the second paper in a series of three papers. In the first paper of the series, "Artinian Gorenstein algebras with linear resolutions", (arXiv:1306.2523, J. of Algebra, to appear) we prove that it is possible to give the minimal resolution of the rings from the title in terms of the coefficients of the corresponding Macaulay inverse system. In this context, the word "give" means, "give in a polynomial manner". The first paper in the series proves, essentially, an existence theorem. The second and third papers in the series construct the explicit formulas for the resolution. The present paper is concerned with Artinian Gorenstein algebras of embedding codimension three. In the third paper, "The structure of Gorenstein-linear resolutions of Artinian algebras", the embedding codimension is arbitrary.