Almost Gorenstein Rees algebras of $p_g$-ideals, good ideals, and powers of the maximal ideals

Abstract

Let $(A,\mathfrak{m})$ be a Cohen-Macaulay local ring and let $I$ be an ideal of $A$. We prove that the Rees algebra $\mathcal{R}(I)$ is an almost Gorenstein ring in the following cases: (1) $(A,\mathfrak{m})$ is a two-dimensional excellent Gorenstein normal domain over an algebraically closed field $K\cong A/\mathfrak{m}$ and $I$ is a $p_g$-ideal; (2) $(A,\mathfrak{m})$ is a two-dimensional almost Gorenstein local ring having minimal multiplicity and $I={\mathfrak{m}}^{\ell }$ for all $\ell \ge 1$; (3) $(A,\mathfrak{m})$ is a regular local ring of dimension $d\ge 2$ and $I={\mathfrak{m}}^{d-1}$. Conversely, if $\mathcal{R}({\mathfrak{m}}^{\ell })$ is an almost Gorenstein graded ring for some $\ell \ge 2$ and $d\ge 3$, then $\ell =d-1$.

14 pages, and the title of this article was changed on 26, June, 2017

References in corpus (2)

• Rees algebras and $p_g$-ideals in a two-dimensional normal local domain
• A characterization of two-dimensional rational singularities via Core of ideals

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• On the almost Gorenstein property of determinantal rings
• Ulrich ideals and 2-AGL rings