Angela Ortega
"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 non-emptiness of such
spaces, including those obtained in a joint work with Brambila-Paz in the
case when the number of sections is bigger than the rank.