A Torelli type theorem for the moduli space of rank two connections on a curve

Indranil Biswas; Jan Nagel

doi:10.1016/j.crma.2005.09.043

Algebraic Geometry

A Torelli type theorem for the moduli space of rank two connections on a curve

Presented by: Jean-Pierre Demailly

Indranil Biswas ¹; Jan Nagel ²

¹ School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India
² Université Lille 1, département de mathématiques, bâtiment M2, 59655 Villeneuve d'Ascq cedex, France

Comptes Rendus. Mathématique, Volume 341 (2005) no. 10, pp. 617-622.

Abstract
Résumé

Let $(X, x_{0})$ be a pointed Riemann surface of genus $g ⩾ 4$ , and let $M_{X}$ be the moduli space parameterizing logarithmic $SL (2, C)$ -connections on X that are singular exactly over $x_{0}$ and have residue $- Id / 2$ . We show that the moduli space $M_{X}$ determines X up to isomorphism.

Soit $(X, x_{0})$ une surface de Riemann pointée de genre $g ⩾ 4$ , et soit $M_{X}$ l'espace des modules des $SL (2, C)$ -connexions logarithmiques qui ont une singularité exactement en $x_{0}$ et ont pour résidu $- Id / 2$ . On démontre que l'espace des modules $M_{X}$ détermine X à isomorphisme près.

Received: 2005-06-24
Accepted: 2005-09-26
Published online: 2005-10-28

DOI: 10.1016/j.crma.2005.09.043

Author's affiliations:

Indranil Biswas ¹; Jan Nagel ²

¹ School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India
² Université Lille 1, département de mathématiques, bâtiment M2, 59655 Villeneuve d'Ascq cedex, France

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     title = {A {Torelli} type theorem for the moduli space of rank two connections on a curve},
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     pages = {617--622},
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     language = {en},
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Indranil Biswas; Jan Nagel. A Torelli type theorem for the moduli space of rank two connections on a curve. Comptes Rendus. Mathématique, Volume 341 (2005) no. 10, pp. 617-622. doi : 10.1016/j.crma.2005.09.043. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.09.043/

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