Bradlow, S.B.García Prada, O.Muñoz, VicenteNewstead, P. E.2023-06-202023-06-2020030129-167X10.1142/S0129167X03002009https://hdl.handle.net/20.500.14352/50629Let X be a curve of genus g. A coherent system on X consists of a pair (E; V ), where E is an algebraic vector bundle over X of rank n and degree d and V is a subspace of dimension k of the space of sections of E. The stability of the coherent system depends on a parameter a. We study the variation of the moduli space of coherent systems when we move the parameter. As an application, we analyze the cases k = 1; 2; 3 and n = 2 explicitly. For small values of , the moduli spaces of coherent systems are related to the Brill-Noether loci, the subschemes of the moduli spaces of stable bundles consisting of those bundles with at least a prescribed number of independent sections. The study of coherent systems is applied to nd the dimension, prove the irreducibility, and in some cases calculate the Picard groups of the Brill{Noether loci with k < 3.engjournal articlehttp://www.worldscientific.com/doi/pdf/10.1142/S0129167X03002009http://www.worldscientific.comhttp://arxiv.orgrestricted access512.7Algebraic curvesModuli of vector bundlesCoherent systemsBrill-Noetherloci.Geometria algebraica1201.01 Geometría Algebraica