# Nefness of the direct images of relative canonical bundles

## TL;DR

This paper investigates the conditions under which the direct images of relative canonical bundles, twisted by pseudo-effective line bundles, are nef, contributing to the understanding of positivity properties in algebraic geometry.

## Contribution

It provides new results on the nefness of direct images of relative canonical bundles twisted by pseudo-effective line bundles with mild singularities.

## Key findings

- Establishes nefness criteria for direct images of relative canonical bundles
- Extends previous results to line bundles with mild singularities
- Provides applications to the geometry of fibrations

## Abstract

Given a fibration $f$ between two projective manifolds $X$ and $Y$, we discuss the nefness of the direct images $f_{\ast}(K_{X/Y}\otimes L)$, where $(L,h)$ is a pseudo-effective line bundle with mild singularity.