When are the Rees algebras of parameter ideals almost Gorenstein graded rings?

Abstract

Let $A$ be a Cohen–Macaulay local ring with $dimA=d\ge 3$, possessing the canonical module ${\mathrm{K}}_A$. Let $a_1,a_2,\dots ,a_r$ $(3\le r\le d)$ be a subsystem of parameters of $A$, and set $Q=(a_1,a_2,\dots ,a_r)$. We show that if the Rees algebra $\mathcal{R}\left(Q\right)$ of $Q$ is an almost Gorenstein graded ring, then $A$ is a regular local ring and $a_1,a_2,\dots ,a_r$ is a part of a regular system of parameters of $A$.