| The Brill-Noether problem for higher rank is concerned with
describing the moduli space of stable vector bundles over a curve
having a prescribed number of sections. One way of studying this
problem is via coherent systems, that is, pairs (E,V) consisting of a
vector bundle E and a subspace V of global sections subject to a
stability condition. In this talk we will mention some generalities about the moduli space of coherent systems and present results on the nonemptiness of such spaces, including recent joint work with Brambila-Paz in the case when the number of sections is bigger than the rank. |