Discreteness of 𝐹-jumping numbers at isolated non-ℚ-Gorenstein points

Abstract

We show that the F F -jumping numbers of a pair ( X , a ) (X, \mathfrak {a}) in positive characteristic have no limit points whenever the symbolic Rees algebra of − K X -K_X is finitely generated outside an isolated collection of points. We also give a characteristic zero version of this result, as well as a generalization of the Hartshorne–Speiser–Lyubeznik–Gabber stabilization theorem describing the non- F F -pure locus of a variety.