The Brill-Noether problem and Teixidor theorem

Let C be a smooth projective algebraic curve of genus g. The Brill-Noether problem is to determine at which conditions on n, d and k, there exists a s table vector bundle of rank n, degree d and with at least k independent glo bal sections. Teixidor gave a rather general answer about the existence in her paper [Tei]. The result was available only for a generic curve, in a ve ry imprecise sense, and the pl oof was really difficult. We show here, that the result is in fact true for all curves and a little more.