Seminormal graded rings and weakly normal projective varieties (Q1076078)

Let \(R=\oplus R_ n\), \(n\in {\mathbb{Z}}\), be a reduced graded ring with finitely many minimal primes. For d a positive integer, let \(R(d)=\oplus R_{nd}\), \(n\in {\mathbb{Z}}\). If \({}^+R\) is the seminormalization of R, it is shown that \({}^+R\) is a graded ring, and that \((^+R)(d)\) is the seminormalization of R(d). Using these and related facts, the paper then shows that the weak normalization of a projective variety is a projective variety.