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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

PDF
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Official URL: http://www.worldscientific.com/doi/pdf/10.1142/S0129167X03002009

URL | URL Type |
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http://www.worldscientific.com | Publisher |

http://arxiv.org | Organisation |

## Abstract

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 |
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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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