Almost Gorenstein Rees Algebras of Pg-Ideals, Good Ideals, and Powers of the Maximal Ideals

Let (A, m) be a Cohen Macaulay local ring, and let I be an ideal of A. We prove that the Rees algebra R(I) is an almost Gorenstein ring in the following cases: (1) (A, m) is a two-dimensional excellent Gorenstein normal domain over an algebraically closed field K congruent to A/m, and I is a p(g)-ideal; (2) (A, m) is a two-dimensional almost Gorenstein local ring having minimal multiplicity, and I = m(l) for all l >= 1; (3) (A, m) is a regular local ring of dimension d >= 2, and I = m(d-1). Conversely, if R(m(l)) is an Gorenstein graded ring for some l >= 2 and d >= 3, then t = d - 1.