Nearly Gorenstein local rings defined by maximal minors of a $2 \times n$ matrix

TL;DR

This paper studies nearly Gorenstein local rings formed by maximal minors of a specific 2xN matrix over a power series ring, providing examples that distinguish nearly Gorenstein from almost Gorenstein rings.

Contribution

It characterizes nearly Gorenstein property for rings defined by maximal minors of a 2xN matrix, offering new explicit examples and distinctions from almost Gorenstein rings.

Findings

Identifies conditions for nearly Gorenstein property in these rings.

Provides examples of nearly Gorenstein rings not almost Gorenstein.

Provides examples of almost Gorenstein rings that are not nearly Gorenstein.

Abstract

We investigate the nearly Gorenstein property of a local ring defined by the maximal minors of a specific $2 \times n$ matrix with entries in the formal power series ring $k[[X_1, X_2, \ldots , X_n]]$ over a field $k$. Our findings allow us to present numerous concrete examples, such as nearly Gorenstein rings that are not almost Gorenstein and vice versa.