# Algebraic fiber spaces and curvature of higher direct images

## TL;DR

This paper investigates the curvature properties of higher direct images of sheaves of differentials in algebraic geometry, providing explicit formulas and applications to families of polarized varieties.

## Contribution

It derives explicit curvature formulas for higher direct images under certain conditions and applies these to prove a key result in the context of polarized families.

## Key findings

- Explicit curvature formulas for higher direct images.
- Application to Viehweg-Zuo's result on polarized families.
- Enhanced understanding of geometric properties of algebraic fiber spaces.

## Abstract

In this article we are interested in the differential geometric properties of certain higher direct images of exterior powers of the sheaf of relative differentials twisted with a line bundle. We obtain explicit curvature formulas, especially in case where the said line bundle satisfies a natural curvature assumption. Several applications are obtained, including a proof of a result by Viehweg-Zuo in the context of a canonically polarized family of maximal variation.