Nefness of the direct images of pluricanonical bundles

Abstract

Given a fibration $f$ between two projective manifolds $X$ and $Y$, we provide a sufficient condition such that the direct images $f_{\ast }(K_{X/Y}\otimes L\otimes \mathcal{I}(f,\Vert L\Vert ))$ is nef, where $L$ is a holomorphic line bundle with non-negative relative Iitaka dimension and $\mathcal{I}(f,\Vert L\Vert )$ is the relative asymptotic multiplier ideal sheaf.

This paper is a refined version of my previous work 1906.07885. Comments welcome!

References in corpus (1)

• A Nadel-type vanishing theorem concerning the asymptotic multiplier ideal sheaf