## 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 fc of the space of sections of E. The stability of the coherent system depends on a parameter α. 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 α, 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 find the dimension, prove the irreducibility, and in some cases calculate the Picard groups of the Brill-Noether loci with k ≤ 3.

Original language | English (US) |
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Pages (from-to) | 683-733 |

Number of pages | 51 |

Journal | International Journal of Mathematics |

Volume | 14 |

Issue number | 7 |

DOIs | |

State | Published - Sep 2003 |

## Keywords

- Algebraic curves
- Brill-Noether loci
- Coherent systems
- Moduli of vector bundles

## ASJC Scopus subject areas

- Mathematics(all)