# Rationality of Rigid Quiver Grassmannians

## TL;DR

This paper proves that quiver Grassmannians linked to rigid quiver representations are rational varieties, utilizing torus localization techniques to establish their rationality.

## Contribution

It introduces a novel proof that all quiver Grassmannians for rigid representations are rational, expanding understanding of their geometric properties.

## Key findings

- All rigid quiver Grassmannians are rational varieties.
- Torus localization techniques effectively prove rationality.
- Provides new insights into the geometry of quiver Grassmannians.

## Abstract

We show that any quiver Grassmannian associated with a rigid representation of a quiver is a rational variety using torus localization techniques.