On the geometry of moduli spaces of coherent systems on algebraic curves.
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...
| Autores: | , , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2007 |
| País: | España |
| Institución: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/50593 |
| Acceso en línea: | https://hdl.handle.net/20.500.14352/50593 |
| Access Level: | acceso abierto |
| Palabra clave: | 512.7 Algebraic curves Moduli of vector bundles Coherent systems Brill–Noether loci Geometria algebraica 1201.01 Geometría Algebraica |
| Sumario: | 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. |
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