Computing structure constants for rings of finite rank from minimal free resolutions

TL;DR

This paper demonstrates how minimal free resolutions of points in projective space can explicitly determine structure constants for rings of finite rank, generalizing classical constructions for specific small ranks.

Contribution

It introduces a method to compute ring structure constants from minimal free resolutions, extending known cases to arbitrary rank n.

Findings

Explicit determination of structure constants from free resolutions

Generalization of classical constructions to higher ranks

Provides a new computational approach for ring structures

Abstract

We show how the minimal free resolution of a set of $n$ points in general position in projective space of dimension $n-2$ explicitly determines structure constants for a ring of rank $n$. This generalises previously known constructions of Levi-Delone-Faddeev and Bhargava in the cases $n=3,4,5$.