Coherent systems and Brill-Noether theory.



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Bradlow, S.B. and García Prada, O. and Muñoz, Vicente and Newstead, P. E. (2003) Coherent systems and Brill-Noether theory. International journal of mathematics, 14 (7). pp. 683-733. ISSN 0129-167X

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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.

Item Type:Article
Uncontrolled Keywords:Algebraic curves; Moduli of vector bundles; Coherent systems; Brill-Noetherloci.
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:21268
Deposited On:08 May 2013 13:50
Last Modified:12 Dec 2018 15:13

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