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Torelli theorem for moduli spaces of SL(r,C) -connections on a compact Riemann surface.

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Biswas, Indranil and Muñoz, Vicente (2009) Torelli theorem for moduli spaces of SL(r,C) -connections on a compact Riemann surface. Communications in contemporary mathematics, 11 (1). pp. 1-26. ISSN 0219-1997

Official URL: http://www.worldscientific.com/doi/abs/10.1142/S0219199709003260


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Abstract

Let X be any compact connected Riemann surface of genus g, with g ≥ 3. For any r ≥ 2, let denote the moduli space of holomorphic SL(r,ℂ)-connections over X. It is known that the biholomorphism class of the complex variety is independent of the complex structure of X. If g = 3, then we assume that r ≥ 3. We prove that the isomorphism class of the variety determines the Riemann surface X uniquely up to an isomorphism. A similar result is proved for the moduli space of holomorphic GL(r,ℂ)-connections on X.


Item Type:Article
Uncontrolled Keywords:Holomorphic connection; Moduli space; Torelli theorem
Subjects:Sciences > Mathematics > Algebraic geometry
ID Code:21030
Deposited On:24 Apr 2013 13:07
Last Modified:12 Dec 2018 15:13

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