Le probleme de Brill-Noether et le theoreme de Teixidor

摘要

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 #kappa#, there exists a stable vector bundle of rank n, degree d and with at least #kappa# independent global 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 very imprecise sense, and the proof was really difficult. We show here, that the result is in fact true for all curves and a little more.