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

Biswas, Indranil; Nagel, Jan

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
[Un théorème de type Torelli pour l'espace des modules des couples de rang deux sur une courbe]

Présenté par : Jean-Pierre Demailly

Biswas, Indranil ¹ ; Nagel, Jan 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, Tome 341 (2005) no. 10, pp. 617-622.

Résumé
Abstract

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.

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.

Reçu le : 2005-06-24
Accepté le : 2005-09-26
Publié le : 2005-10-28

DOI : 10.1016/j.crma.2005.09.043

Affiliations des auteurs :

Biswas, Indranil ¹ ; Nagel, Jan ²

@article{CRMATH_2005__341_10_617_0,
     author = {Biswas, Indranil and Nagel, Jan},
     title = {A {Torelli} type theorem for the moduli space of rank two connections on a curve},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {617--622},
     publisher = {Elsevier},
     volume = {341},
     number = {10},
     year = {2005},
     doi = {10.1016/j.crma.2005.09.043},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2005.09.043/}
}

TY  - JOUR
AU  - Biswas, Indranil
AU  - Nagel, Jan
TI  - A Torelli type theorem for the moduli space of rank two connections on a curve
JO  - Comptes Rendus. Mathématique
PY  - 2005
SP  - 617
EP  - 622
VL  - 341
IS  - 10
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2005.09.043/
DO  - 10.1016/j.crma.2005.09.043
LA  - en
ID  - CRMATH_2005__341_10_617_0
ER  -

%0 Journal Article
%A Biswas, Indranil
%A Nagel, Jan
%T A Torelli type theorem for the moduli space of rank two connections on a curve
%J Comptes Rendus. Mathématique
%D 2005
%P 617-622
%V 341
%N 10
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2005.09.043/
%R 10.1016/j.crma.2005.09.043
%G en
%F CRMATH_2005__341_10_617_0

Biswas, Indranil; Nagel, Jan. A Torelli type theorem for the moduli space of rank two connections on a curve. Comptes Rendus. Mathématique, Tome 341 (2005) no. 10, pp. 617-622. doi : 10.1016/j.crma.2005.09.043. http://www.numdam.org/articles/10.1016/j.crma.2005.09.043/

Bibliographie
Cité par

[1] Arbarello, E.; Cornalba, M.; Griffiths, P.A.; Harris, J. Geometry of Algebraic Curves, I, Springer-Verlag, New York, 1985

[2] I. Biswas, N. Raghavendra, Line bundles over a moduli space of logarithmic connections on a Riemann surface, Geom. Funct. Anal., in press

[3] Borel, A. Density properties for certain subgroups of semi-simple groups without compact components, Ann. of Math., Volume 72 (1960), pp. 179-188

[4] Carlson, J. Extensions of mixed Hodge structures, Journées de géométrie algébrique d'Angers 1979, Sijthoff & Noordhoff, Alphen aan den Rijn, 1980, pp. 107-127

[5] Deligne, P. Equations Différentielles à Points Singuliers Réguliers, Lecture Notes in Math., vol. 163, Springer-Verlag, Berlin, 1970

[6] Hitchin, N.J. The self-duality equations on a Riemann surface, Proc. Lond. Math. Soc., Volume 55 (1987), pp. 59-126

[7] Mumford, D.; Newstead, P.E. Periods of a moduli space of bundles on curves, Amer. J. Math., Volume 90 (1968), pp. 1200-1208

[8] Newstead, P. Topological properties of some spaces of stable bundles, Topology, Volume 6 (1967), pp. 241-262

[9] Narasimhan, M.S.; Seshadri, C.S. Stable and unitary vector bundles on a compact Riemann surface, Ann. of Math., Volume 82 (1965), pp. 540-567

[10] Nitsure, N. Moduli of semistable logarithmic connections, J. Amer. Math. Soc., Volume 6 (1993), pp. 597-609

[11] Simpson, C.T. Moduli of representations of the fundamental group of a smooth projective variety. I, Inst. Hautes Études Sci. Publ. Math., Volume 79 (1994), pp. 47-129

Cité par Sources :