Existence results on moduli spaces of coherent systems

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.