Petri map for vector bundles near good bundles

Let C be a projective nonsingular curve of genus g and let Br,dk be the locus of stable rank r degree d vector bundles with at least k linearly independent sections on C. It is known that when C is general and under certain conditions on g, d, r, and k, there exists a component B of Br,dk of the expected dimension. In this paper we show that for a general vector bundle E of B, the Petri map is injective.