Non-emptiness of Brill-Noether loci over very general quintic hypersurface

In this article we study Brill-Noether loci of moduli space of stable bundles over smooth surfaces. We define Petri map as an analogy with the case of curves. We show the non-emptiness of certain Brill-Noether loci over very general quintic hypersurface in P3, and use the Petri map to produce components of expected dimension.