A. Langer

Stability of vector bundles and reduction mod $p$

Let $E$ be a vector bundle on a normal complex projective variety. We prove that slope stability of $\mathop{Sym}^2E$ and Zariski density of the reductions of $E$ modulo $p$ that are not strongly geometrically stable imply that the bundle $E$ is projectively unitary flat. This generalizes Shepherd--Barron's result from...