# A remark on rationally connected varieties and Mori dream spaces

## TL;DR

This paper demonstrates that certain rationally connected varieties, constructed by Ottem, are not birationally equivalent to Mori dream spaces, answering a question about their relationship.

## Contribution

It provides a counterexample showing rationally connected varieties need not be Mori dream spaces, clarifying their relationship in algebraic geometry.

## Key findings

- Counterexample of a rationally connected variety not birationally equivalent to a Mori dream space
- Answers Krylov's question negatively in the category of terminal varieties
- Highlights limitations of Mori dream space classification

## Abstract

In this short note, we show that a construction by Ottem provides an example of a rationally connected variety that is not birationally equivalent to a Mori dream space. This answers in the negative (at least in the category of terminal varieties) a question posed by Krylov.