  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.
