# Chern numbers of uniruled threefolds

## TL;DR

This paper proves that the Chern numbers of certain three-dimensional algebraic varieties are bounded by their underlying topology, extending previous results to cases with negative Kodaira dimension.

## Contribution

It establishes bounds on Chern numbers for smooth Mori fibre spaces and generalizes existing theorems to broader classes of threefolds.

## Key findings

- Chern numbers of smooth Mori fibre spaces are topologically bounded.
- Extended boundedness results to threefolds with negative Kodaira dimension.
- Provides new insights into the relationship between topology and algebraic geometry in threefolds.

## Abstract

In this paper we show that the Chern numbers of a smooth Mori fibre space in dimension three are bounded in terms of the underlying topological manifold. We also generalise a theorem of Cascini and the second named author on the boundedness of Chern numbers of certain threefolds to the case of negative Kodaira dimension.