A note on the existence of certain rank 2 stable bundles on very general hypersurfaces of degree at least 5 in P3

Let X subset of P-3 be a very general hypersurface of degree >= 5. In this paper, using two different methods, we study the existence of certain rank 2 stable bundles over X with a view towards the geometry of their Brill-No ether loci. In the first method, we establish the existence of certain specific base point free line bundles on some smooth curves lying on X. We then use this study and the notion of "Mukai exact sequence" to obtain stable bundles of rank 2 on X. Generalized study of dimension estimate of potentially obstructed bundles then tells us that these rank 2 bundles are smooth points in the corresponding moduli spaces. We also show that in some specific cases, the smoothness of the Brill-No ether loci of line bundles on such curves gives us the smoothness of the Brill-No ether loci of rank 2 bundles on X. In the second method, we use "Serre correspondence" to produce rank 2 stable bundles over X. Finally, applying techniques from moduli theory, we obtain results on their Brill-No ether loci.