The almost Gorenstein Rees algebras of parameters

TL;DR

This paper characterizes when Rees algebras of parameters in Gorenstein local rings are almost Gorenstein, and explores the rarity of such algebras for socle ideals in higher dimensions.

Contribution

It provides new characterizations for almost Gorenstein Rees algebras of parameters and socle ideals, highlighting their scarcity in higher-dimensional rings.

Findings

Rees algebras of parameters can be characterized as almost Gorenstein in Gorenstein local rings.

Almost Gorenstein Rees algebras of socle ideals are rare in rings of dimension greater than two.

The paper offers criteria to identify when Rees algebras are almost Gorenstein.

Abstract

There is given a characterization for the Rees algebras of parameters in a Gorenstein local ring to be almost Gorenstein graded rings. A characterization is also given for the Rees algebras of socle ideals of parameters. The latter one shows almost Gorenstein Rees algebras rather rarely exist for socle ideals, if the dimension of the base local ring is greater than two.