Ample stable vector bundles on rational surfaces

We study ample stable vector bundles on minimal rational surfaces. give a complete classification of those moduli spaces for which the general bundle is both and globally generated. also prove that if V any bundle, then large enough direct sum V⊕n has deformations unless there an obvious numerical reason why it cannot. Previous work in this area mostly focused rank two relied primarily classical sconstructions such as Serre construction. In contrast, we use recent advances to obtain strong results rank.