Poincaré families and automorphisms of principal bundles on a curve

Indranil Biswas; Norbert Hoffmann

doi:10.1016/j.crma.2009.10.006

Algebraic Geometry

Poincaré families and automorphisms of principal bundles on a curve

Presented by: Gérard Laumon

Indranil Biswas ¹; Norbert Hoffmann ²

¹ School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
² Mathematisches Institut der Freien Universität, Arnimallee 3, 14195 Berlin, Germany

Comptes Rendus. Mathématique, Volume 347 (2009) no. 21-22, pp. 1285-1288.

Abstract
Résumé

Let C be a smooth projective curve, and let G be a reductive algebraic group. We give a necessary condition, in terms of automorphism groups of principal G-bundles on C, for the existence of Poincaré families parameterized by Zariski-open parts of their coarse moduli schemes. Applications are given for the moduli spaces of orthogonal and symplectic bundles.

Soit C une courbe projective lisse, et soit G un groupe algébrique réductif. On donne une condition nécessaire, en termes de groupes d'automorphismes des G-fibrés principaux sur C, pour l'existence des familles de Poincaré paramétrées par des ouverts de Zariski dans leurs schémas de modules grossiers. On donne des applications pour les espaces de modules des fibrés orthogonaux et symplectiques.

Received: 2009-08-20
Accepted: 2009-09-29
Published online: 2009-10-24

DOI: 10.1016/j.crma.2009.10.006

Author's affiliations:

Indranil Biswas ¹; Norbert Hoffmann ²

¹ School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400005, India
² Mathematisches Institut der Freien Universität, Arnimallee 3, 14195 Berlin, Germany

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     author = {Indranil Biswas and Norbert Hoffmann},
     title = {Poincar\'e families and automorphisms of principal bundles on a curve},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1285--1288},
     publisher = {Elsevier},
     volume = {347},
     number = {21-22},
     year = {2009},
     doi = {10.1016/j.crma.2009.10.006},
     language = {en},
}

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Indranil Biswas; Norbert Hoffmann. Poincaré families and automorphisms of principal bundles on a curve. Comptes Rendus. Mathématique, Volume 347 (2009) no. 21-22, pp. 1285-1288. doi : 10.1016/j.crma.2009.10.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.10.006/

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