Brill-Noether loci over very general quintic hypersurface

Brill-Noether loci of moduli space of stable bundles over irreducible, smooth, projective variety (over complex numbers) was constructed by L. Costa and R.M. Miro-Roig. This is a generalization of classical Brill-Noether loci over curves. In this talk, we will briefly outline this construction, and define “Petri map” over surfaces, as an analogue of the case of curves. We will discuss how one can use this Petri map to show non-emptiness of certain Brill-Noether loci. This is a joint work with Sarbeswar Pal.