A finiteness property of graded sequences of ideals

Abstract

Given a graded sequence of ideals ${\left({\mathfrak{a}}_m\right)}_{m\ge 1}$ on $X$, having finite log canonical threshold, we show that if there are divisors $E_m$ over $X$ computing the log canonical threshold of ${\mathfrak{a}}_m$, and such that the log discrepancies of the divisors $E_m$ are bounded, then the set $\left\{E_m\mid m\ge 1\right\}$ is finite.