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

Abstract We investigate the nearly Gorenstein property of a local ring defined by the maximal minors of a specific $$2 \times n$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mn>2</mml:mn> <mml:mo>×</mml:mo> <mml:mi>n</mml:mi> </mml:mrow> </mml:math> matrix with entries in the formal power series ring $$k[[X_1, X_2, \ldots , X_n]]$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>k</mml:mi> <mml:mo>[</mml:mo> <mml:mrow> <mml:mo>[</mml:mo> <mml:msub> <mml:mi>X</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>X</mml:mi> <mml:mn>2</mml:mn> </mml:msub> <mml:mo>,</mml:mo> <mml:mo>…</mml:mo> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>X</mml:mi> <mml:mi>n</mml:mi> </mml:msub> <mml:mo>]</mml:mo> </mml:mrow> <mml:mo>]</mml:mo> </mml:mrow> </mml:math> 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.