A characterization of nef and good divisors by asymptotic multiplier ideals

Abstract

A characterization of nef and good divisors is given: a divisor $D$ on a smooth complex projective variety is nef and good if and only if the asymptotic multiplier ideals of sufficiently high multiples of $e(D)\cdot D$ are trivial, where $e(D)$ denotes the exponent of the divisor $D$. Some results of the same kind are proved in the analytic setting.