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Biswas, Indranil and Muñoz, Vicente
(2010)
*Moduli spaces of connections on a Riemann surface.*
In
Teichmüller theory and.
Ramanujan Mathematical Society
(10).
International Press, Massachusetts, U.S.A, pp. 95-111.
ISBN 978-1-57146-195-7

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## Abstract

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.

Item Type: | Book Section |
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Additional Information: | Proceedings of the U.S.-India workshop in Teichmüller theory and moduli problems,Harish-Chandra Research Institute, Allahabad, January 2006 |

Subjects: | Sciences > Mathematics > Algebraic geometry |

ID Code: | 20864 |

Deposited On: | 16 Apr 2013 16:17 |

Last Modified: | 12 Dec 2018 15:13 |

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