%0 Journal Article
%A Bradlow, S.B.
%A García Prada, O.
%A Mercat, V.
%A Muñoz, Vicente
%A Newstead, P. E.
%T On the geometry of moduli spaces of coherent systems on algebraic curves.
%D 2007
%@ 0129-167X
%U https://hdl.handle.net/20.500.14352/50593
%X Let 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 thevariation 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 groupsof 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 thecase k = n − 2. In an appendix, we describe the geometry of the “flips” which takeplace at critical values of a in the simplest case, and include a proof of the existenceof universal families of coherent systems when GCD(n, d, k)= 1.
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