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oai:docta.ucm.es:20.500.14352/506292023-08-10T21:02:28Zcom_20.500.14352_14col_20.500.14352_15

Coherent systems and Brill-Noether theory. Bradlow, S.B. García Prada, O. Muñoz, Vicente Newstead, P. E. 512.7 Algebraic curves Moduli of vector bundles Coherent systems Brill-Noetherloci. Geometria algebraica 1201.01 Geometría Algebraica Let 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. EAGER EDGE Acciones Integradas Programme National Science Foundation Depto. de Álgebra, Geometría y Topología Fac. de Ciencias Matemáticas TRUE pub 2023-06-20T10:34:46Z 2023-06-20T10:34:46Z 2003 journal article https://hdl.handle.net/20.500.14352/50629 0129-167X 10.1142/S0129167X03002009 eng HPRN-CT-2000-00099 HPRN-CT-2000-00101 HB 1998-0006 DMS-0072073 restricted access application/pdf World Scientific