# On the Cheltsov--Rubinstein conjecture

## TL;DR

This paper examines the Cheltsov--Rubinstein conjecture, demonstrating that it does not hold universally by providing counterexamples that challenge its validity.

## Contribution

The paper provides the first known counterexamples to the Cheltsov--Rubinstein conjecture, showing its limitations and prompting reconsideration of related conjectural frameworks.

## Key findings

- Counterexamples disprove the conjecture in general
- The conjecture does not hold universally
- Implications for future research in the area

## Abstract

In this note we investigate the Cheltsov--Rubinstein conjecture. We show that this conjecture does not hold in general and some counterexamples will be presented.