# Frobenius induced morphisms on moduli of sheaves on curves

## TL;DR

This paper proves that the Frobenius pullback preserves semi-stability for general vector bundles on curves and explores various applications of this result.

## Contribution

It establishes the semi-stability preservation under Frobenius pullback for general bundles and introduces multiple applications of this theorem.

## Key findings

- Frobenius pullback preserves semi-stability for general bundles
- Deformation trick used to prove main theorem
- Several applications derived from the main result

## Abstract

We show the Frobenius pullback of a general semi-stable vector bundle in the moduli space of vector bundles with fixed rank and degree is still semi-stable by deformation trick. We then present several applications of the main theorem.