The almost Gorenstein conjecture for Rees algebras of $p_g$-ideals

Let $A$ be the two-dimensional normal local ring under consideration, let $I\subset A$ be a $p_g$-ideal, and let $\mathcal{R}(I)=\bigoplus_{n\geq 0}I^nt^n$ denote its Rees algebra with the standard grading. Almost Gorenstein Rees algebra conjecture. If $I\subset A$ is a $p_g$-ideal, then $\mathcal{R}(I)$ is an almost Gorenstein graded ring. The conjecture extends the known fact that the Rees algebra of a $p_g$-ideal is a Cohen–Macaulay normal domain; it concerns whether this Rees algebra also satisfies the stronger almost Gorenstein property.