Mathematical Research Letters

Volume 30 (2023)

Number 4

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

Pages: 1011 – 1044

DOI: https://dx.doi.org/10.4310/MRL.2023.v30.n4.a2

Authors

Tom Fisher (DPMMS, University of Cambridge, Centre for Mathematical Sciences, Cambridge, United Kingdom)

Lazar Radičević (DPMMS, University of Cambridge, Centre for Mathematical Sciences, Cambridge, United Kingdom)

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 $n = 3, 4, 5$.

Full Text (PDF format)

Received 1 October 2021

Received revised 28 June 2022

Accepted 17 December 2022

Published 3 April 2024