# Rationality of $\mathbb{Q}$-Fano threefolds of large Fano index

## TL;DR

This paper proves that all $Q$-Fano threefolds with Fano index at least 8 are rational, establishing a significant classification result in algebraic geometry.

## Contribution

It demonstrates the rationality of $Q$-Fano threefolds with large Fano index, a previously unresolved classification problem.

## Key findings

- All $Q$-Fano threefolds with Fano index ≥ 8 are rational.
- Provides a classification criterion based on Fano index.
- Advances understanding of the structure of Fano threefolds.

## Abstract

We prove that $\mathbb{Q}$-Fano threefolds of Fano index $\ge 8$ are rational.