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

  title={Discreteness of -jumping numbers at isolated non-ℚ-Gorenstein points},
  author={Patrick Graf and Karl Schwede},
We show that the $F$-jumping numbers of a pair $(X, \mathfrak a)$ in positive characteristic have no limit points whenever the symbolic Rees algebra of $-K_X$ 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-$F$-pure locus of a variety.