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

Abstract

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≅A/m, and I is a pg-ideal; (2) (A,m) is a two-dimensional almost Gorenstein local ring having minimal multiplicity, and I=mℓ for all ℓ≥1; (3) (A,m) is a regular local ring of dimension d≥2, and I=md−1. Conversely, if R(mℓ) is an almost Gorenstein graded ring for some ℓ≥2 and d≥3, then ℓ=d−1.