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http://dspace.mediu.edu.my:8181/xmlui/handle/10261/2493| Title: | Moduli spaces of coherent systems of small slope on algebraic curves |
| Keywords: | Algebraic curves Moduli of vector bundles Coherent systems Brill-Noether loci |
| Description: | Let $C$ be an algebraic curve of genus $g\ge2$. 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 $\alpha$. We study the geometry of the moduli space of coherent systems for $0<d\le2n$. We show that these spaces are irreducible whenever they are non-empty and obtain necessary and sufficient conditions for non-emptiness. Support was received from a grant from the European Scientific Exchange Programme of the Royal Society of London and the Consejo Superior de Investigaciones Científicas (15646) and a further grant from the Royal Society of London for an International Joint Project (2005/R3). The first author was partially supported by the National Science Foundation under grant DMS-0072073. The first, second and fourth authors were supported through MEC grant MTM2004-07090-C03-01 (Spain) and the fourth also through NSF grant DMS-0111298 (US). The fifth author was supported by the Academia Mexicana de Ciencias during a visit to CIMAT, Guanajuato, Mexico. Peer reviewed |
| URI: | http://dspace.mediu.edu.my:8181/xmlui/handle/10261/2493 |
| Other Identifiers: | arXiv:0707.0983v1 http://hdl.handle.net/10261/2493 |
| Appears in Collections: | Digital Csic |
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