A structure result for Gorenstein algebras of odd codimension

TL;DR

This paper extends the structure theorem for Gorenstein ideals of codimension 3 to Gorenstein algebras of any odd codimension, providing a broader understanding of their minimal free resolutions.

Contribution

It generalizes Buchsbaum and Eisenbud's structure theorem from ideals to algebras of odd codimension, offering a new classification framework.

Findings

Describes Gorenstein algebras of odd codimension

Provides a new perspective on minimal free resolutions

Analyzes the canonical ring of a numerical Godeaux surface

Abstract

The famous structure theorem of Buchsbaum and Eisenbud gives a complete characterization of Gorenstein ideals of codimension 3 and their minimal free resolutions. We generalize the ideas of Buchsbaum and Eisenbud from Gorenstein ideals to Gorenstein algebras and present a description of Gorenstein algebras of any odd codimension. As an application we study the canonical ring of a numerical Godeaux surface.