Let be a Cohen–Macaulay local ring, and let be an ideal of . We prove that the Rees algebra is an almost Gorenstein ring in the following cases:
(1) is a two-dimensional excellent Gorenstein normal domain over an algebraically closed field , and is a -ideal;
(2) is a two-dimensional almost Gorenstein local ring having minimal multiplicity, and for all ;
(3) is a regular local ring of dimension , and . Conversely, if is an almost Gorenstein graded ring for some and , then .
"Almost Gorenstein Rees Algebras of -Ideals, Good Ideals, and Powers of the Maximal Ideals." Michigan Math. J. 67 (1) 159 - 174, March 2018. https://doi.org/10.1307/mmj/1516330972