Frobenius induced morphisms on moduli of sheaves on curves

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.

In the first version of this work, we mistakenly claimed that there are only finitely many isomorphism classes of bundles whose Frobenius pullback yields an isomorphic bundle. The editor kindly pointed out counterexamples to this statement such as in Pauly07, Proposition 4.1, Pauly provided an explicit example of such a family