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 $\ell=d-1$.
Categories: math.AC