# On RC varieties without smooth rational curves

## TL;DR

This paper constructs high-dimensional rationally connected varieties that notably lack any smooth rational curves, challenging previous assumptions about their geometric properties.

## Contribution

It introduces the first examples of rationally connected varieties without smooth rational curves, expanding understanding of their possible structures.

## Key findings

- Existence of high-dimensional rationally connected varieties without smooth rational curves
- Construction methods for such varieties
- Implications for the geometry of rationally connected varieties

## Abstract

We construct normal rationally connected varieties (of arbitrarily large dimension) not containing any smooth rational curves.