# Some pathologies of Fano manifolds in positive characteristic

## TL;DR

This paper constructs examples of Fano manifolds over fields of positive characteristic that do not exist over the complex numbers, highlighting unique pathologies in positive characteristic algebraic geometry.

## Contribution

It provides explicit examples of Fano manifolds in positive characteristic that cannot be realized over the complex numbers, revealing new pathological behaviors.

## Key findings

- Existence of Fano manifolds in positive characteristic not over complex numbers
- Examples demonstrating pathologies unique to positive characteristic
- Insights into the structure of algebraic varieties in different characteristics

## Abstract

We construct examples of Fano manifolds, which are defined over a field of positive characteristic, but not over $\com$.