A characterization of nef and good divisors by asymptotic multiplier ideals

TL;DR

This paper characterizes nef and good divisors on smooth complex projective varieties using asymptotic multiplier ideals, providing a new criterion that links algebraic and analytic perspectives.

Contribution

It introduces a novel characterization of nef and good divisors via asymptotic multiplier ideals, bridging algebraic and analytic approaches.

Findings

Nef and good divisors are characterized by trivial asymptotic multiplier ideals at high multiples.

The criterion applies to smooth complex projective varieties.

Results extend to the analytic setting.

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) 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.