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Título: | On the geometry of moduli spaces of coherent systems on algebraic curves |
Autor: | Bradlow, Steven B.; García Prada, Oscar; Mercat, V.; Newstead, P.E. | Palabras clave: | Algebraic curves Moduli of vector bundles Coherent systems Brill-Noether loci |
Fecha de publicación: | 2-ago-2006 | Citación: | arXiv:math/0407523v5 | Resumen: | 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 α. We study the geometry of the moduli space of coherent systems for different values of α when k ≤ n and the variation of the moduli spaces when we vary α. As a consequence, for sufficiently large α, 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 Poincaré polynomials for the case k = n − 2. In an appendix, we describe the geometry of the “flips” which take place at critical values of α in the simplest case, and include a proof of the existence of universal families of coherent systems when GCD(n, d, k) = 1. | Descripción: | 38 pages. Nr. 5 is final version (02/08/2006), one typo was corrected and one reference deleted. Version nr. 4 (12/06/2006) included minor corrections and two added references. Version nr. 3 (23/06/2005) had appendix and new references added. | URI: | http://hdl.handle.net/10261/2550 |
Aparece en las colecciones: | (ICMAT) Artículos |
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