The almost Gorenstein Rees algebras over two-dimensional regular local rings

Let (R,m)(R,m) be a two-dimensional regular local ring with infinite residue class field. Then the Rees algebra R(I)=⨁n≥0InR(I)=⨁n≥0In of I is an almost Gorenstein graded ring in the sense of [6] for every mm-primary integrally closed ideal I in R.