Stability of direct images under Frobenius morphism

Abstract

Let $X$ be a smooth projective variety over an algebraically field $k$ with $\mathrm{char}(k)=p>0$ and $F:X\to X_1$ be the relative Frobenius morphism. When $\dim (X)=1$, we prove that $F_{\ast }W$ is a stable bundle for any stable bundle $W$ (Theorem \ref{thm1.3}). As a step to study the question for higher dimensional $X$, we generalize the canonical filtration (defined by Joshi-Ramanan-Xia-Yu for curves) to higher dimensional $X$ (Theorem \ref{thm2.6}).

9 pages, latex, the proof of Theorem 2.3 is simplified

Cited by in corpus (2)

• Direct images of bundles under Frobenius morphisms
• Frobenius inverse image of the semi-stable boundary in the moduli space of vector bundles