On the almost Gorenstein property of determinantal rings

TL;DR

This paper studies when determinantal rings over a field are almost Gorenstein, revealing that non-Gorenstein cases with this property have minimal multiplicity.

Contribution

It characterizes the almost Gorenstein property for determinantal rings and links it to minimal multiplicity in non-Gorenstein cases.

Findings

Determinantal rings are almost Gorenstein only under specific conditions.

Non-Gorenstein almost Gorenstein determinantal rings have minimal multiplicity.

The paper provides criteria for the almost Gorenstein property in this context.

Abstract

In this paper we investigate the question of when the determinantal ring $R$ over a field $k$ is an almost Gorenstein local/graded ring in the sense of Goto, Takahashi, and the author. As a consequence of the main result, we see that if $R$ is a non-Gorenstein almost Gorenstein local/graded ring, then the ring $R$ has a minimal multiplicity.