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

Abstract

Let $A$ be a Cohen-Macaulay local ring with $\dim A=d\ge 3$, 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 $Q=(a_1,a_2,\dots ,a_r)$. It is shown that if the Rees algebra $\mathcal{R}(Q)$ 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 $A$.

arXiv comment9 pages

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