Biswas, Indranil ; Munoz, Vicente
(2007)
*The Torelli theorem for the moduli spaces of connections on a Riemann surface*
Topology, 46
(3).
pp. 295-317.
ISSN 0040-9383

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Official URL: http://linkinghub.elsevier.com/retrieve/pii/S00409...

Related URL: http://dx.doi.org/10.1016/j.top.2007.02.005

## Abstract

Let (X,x_{0}) be any one-pointed compact connected Riemann surface of genus g, with g≥ 3. Fix two mutually coprime integers r>1 and d. Let M_{x} denote the moduli space parametrizing all logarithmic SL(r,C) -connections, singular over x_{0}, on vector bundles over X of degree d. We prove that the isomorphism class of the variety M_{x} determines the Riemann surface X uniquely up to an isomorphism, although the biholomorphism class of is known to be independent of the complex structure of X. The isomorphism class of the variety M_{x} is independent of the point x_{0}∈X. A similar result is proved for the moduli space parametrizing logarithmic GL(r,C)-connections, singular over x_{0}, on vector bundles over X of degree d. The assumption r>1 is necessary for the moduli space of logarithmic GL(r,C)-connections to determine the isomorphism class of X uniquely.

Item Type: | Article |
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Source: | Copyright of this article belongs to Elsevier Science. |

Keywords: | Logarithmic Connection; Moduli Space; Torelli Theorem |

ID Code: | 3617 |

Deposited On: | 18 Oct 2010 10:19 |

Last Modified: | 18 Oct 2010 10:19 |

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