On Frobenius-destabilized rank-2 vector bundles over curves

Let X be a smooth projective curve of genus g ≥ 2 over an algebraically closed field k of characteristic p > 0. Let MX be the moduli space of semistable rank-2 vector bundles over X with trivial determinant. The relative Frobenius map F: X → X₁ induces by pull-back a rational map V: Mₗ䃑 MX. In this paper we show the following results.