# On a theorem of Campana and P\u{a}un

## TL;DR

This paper provides a simplified proof of a theorem linking the positivity of certain sheaves on a log pair to the log general type property, advancing the understanding of Viehweg's hyperbolicity conjecture.

## Contribution

It offers a streamlined proof of a theorem by Campana and Pe2un, crucial for progress on Viehweg's hyperbolicity conjecture.

## Key findings

- Simplified proof of Campana and Pe2un's theorem.
- Establishes a criterion for log general type based on tensor powers of logarithmic differentials.
- Supports the proof of Viehweg's hyperbolicity conjecture.

## Abstract

Let $X$ be a smooth projective variety over the complex numbers, and $\Delta \subseteq X$ a reduced divisor with normal crossings. We present a slightly simplified proof for the following theorem of Campana and P\u{a}un: If some tensor power of the bundle $\Omega_X^1(\log \Delta)$ contains a subsheaf with big determinant, then $(X, \Delta)$ is of log general type. This result is a key step in the recent proof of Viehweg's hyperbolicity conjecture.