# On the Frobenius direct image of the structure sheaf of a homogeneous projective variety

## TL;DR

This paper provides an example of a homogeneous projective variety where the Frobenius direct image of its structure sheaf exhibits nonvanishing self-extensions, highlighting a unique property in algebraic geometry.

## Contribution

It introduces a specific example demonstrating nonvanishing self-extensions of the Frobenius direct image, a novel phenomenon in the study of homogeneous projective varieties.

## Key findings

- Frobenius direct image can have nonvanishing self-extensions.
- Example of a homogeneous projective variety with this property.
- Insights into the structure of sheaves under Frobenius morphism.

## Abstract

We present an example of a homogeneous projective variety the Frobenius direct image of the structure sheaf of which has nonvanishing self extension.