Bradlow, S.B.García Prada, O.Mercat, V.Muñoz, VicenteNewstead, P. E.2023-06-202023-06-2020070129-167X10.1142/S0129167X07004151https://hdl.handle.net/20.500.14352/50593Let C be an algebraic curve of genus g ≥ 2. A coherent system on C consists of a pair (E, V ), where E is an algebraic vector bundle over C 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 geometry of the moduli space of coherent systems for different values of a when k ≤ n and the variation of the moduli spaces when we vary a. As a consequence, for sufficiently large , we compute the Picard groups and the first and second homotopy groups of the moduli spaces of coherent systems in almost all cases, describe the moduli space for the case k = n − 1 explicitly, and give the Poincare polynomials for the case k = n − 2. In an appendix, we describe the geometry of the “flips” which take place at critical values of a in the simplest case, and include a proof of the existence of universal families of coherent systems when GCD(n, d, k)= 1.engjournal articlehttp://www.worldscientific.com/doi/abs/10.1142/S0129167X07004151http://www.worldscientific.comopen access512.7Algebraic curvesModuli of vector bundlesCoherent systemsBrill–Noether lociGeometria algebraica1201.01 Geometría Algebraica