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Bradlow, S.B. and García Prada, O. and Mercat, V. and Muñoz, Vicente and Newstead, P. E.
(2007)
*On the geometry of moduli spaces of coherent systems on algebraic curves.*
International journal of mathematics, 18
(4).
pp. 411-453.
ISSN 0129-167X

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Official URL: http://www.worldscientific.com/doi/abs/10.1142/S0129167X07004151

## Abstract

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 the

variation 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 groups

of 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 the

case k = n − 2. In an appendix, we describe the geometry of the “flips” which take

place at critical values of a in the simplest case, and include a proof of the existence

of universal families of coherent systems when GCD(n, d, k)= 1.

Item Type: | Article |
---|---|

Uncontrolled Keywords: | Algebraic curves; Moduli of vector bundles; Coherent systems; Brill–Noether loci |

Subjects: | Sciences > Mathematics > Algebraic geometry |

ID Code: | 21040 |

Deposited On: | 24 Apr 2013 14:14 |

Last Modified: | 12 Dec 2018 15:13 |

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