| Título: | On the geometry of moduli spaces of coherent systems on algebraic curves. |
| Autores: | Bradlow, S.B. ; García Prada, O. ; Mercat, V. ; Muñoz, Vicente ; Newstead, P. E. |
| Tipo de documento: | texto impreso |
| Editorial: | World Scientific, 2007 |
| Dimensiones: | application/pdf |
| Nota general: | info:eu-repo/semantics/openAccess |
| Idiomas: | |
| Palabras clave: | Estado = Publicado , Materia = Ciencias: Matemáticas: Geometria algebraica , Tipo = Artículo |
| 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 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. |
| En línea: | https://eprints.ucm.es/id/eprint/21040/1/VMu%C3%B1oz37.pdf |
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