Rees algebras and \(p_g\)-ideals in a two-dimensional normal local domain (Q2832805)

This paper contains several characterizations of the so called \(p_g\)-ideals, a class recently introduced by the same authors [Manuscr. Math. 150, No. 3--4, 499--520 (2016; Zbl 1354.13011)]. More precisely, if \(I\) is an \(\mathfrak{m}\)-primary ideal in a two-dimensional excellent normal local domain \((A,\mathfrak{m})\) that contains an algebraically closed field, then \(I\) is a \(p_g\)-ideal if and only if \(I^2=IQ\) for every minimal reduction \(Q\) of \(I\) and all the powers of \(I\) are integrally closed. Equivalently, the Rees algebra \(A[It]\) is a Cohen-Macaulay normal domain.