Moduli spaces of connections on a Riemann surface.
Let E be a holomorphic vector bundle over a compact connected Riemann surface X. The vector bundle E admits a holomorphic projective connection if and only if for every holomorphic direct summand F of E of positive rank, the equality degree(E)=rank(E) = degree(F)=rank(F) holds. Fix a point x0 in X....
| Autores: | , |
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| Formato: | capítulo de livro |
| Fecha de publicación: | 2010 |
| País: | España |
| Recursos: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/45436 |
| Acesso em linha: | https://hdl.handle.net/20.500.14352/45436 |
| Access Level: | acceso abierto |
| Palavra-chave: | 512.7 Geometria algebraica 1201.01 Geometría Algebraica |
| Resumo: | Let E be a holomorphic vector bundle over a compact connected Riemann surface X. The vector bundle E admits a holomorphic projective connection if and only if for every holomorphic direct summand F of E of positive rank, the equality degree(E)=rank(E) = degree(F)=rank(F) holds. Fix a point x0 in X. There is a logarithmic connection on E, singular over x0 with residue ¡d n IdEx0 if and only if the equality degree(E)=rank(E) = degree(F)=rank(F) holds. Fix an integer n ¸ 2, and also ¯x an integer d coprime to n. Let M(n; d) denote the moduli space of logarithmic SL(n;C){connections on X singular of x0 with residue ¡ d n Id. The isomorphism class of the variety M(n; d) determines the isomorphism class of the Riemann surface X. |
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