Geodesic
Analyse et géométrie complexes
Examples of non-flat bundles of rank one
[Exemples de fibrés en droites qui ne sont pas plats]
Dan, Ananyo1  ; Romano-Velázquez, Agustín2, 3
1 School of Mathematics and Statistics, University of Sheffield, Hicks building, Hounsfield Road, S3 7RH, UK
2 Alfréd Rényi Institute Of Mathematics, Hungarian Academy Of Sciences, Reáltanoda Utca 13-15, H-1053, Budapest, Hungary
3 Universidad Nacional Autónoma de México Avenida Universidad s/n, Colonia Lomas de Chamilpa CP 62210, Cuernavaca, Morelos Mexico
Comptes Rendus. Mathématique, Tome 361 (2023) no. G6, pp. 965-968

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It is expected that there exist line bundles on a quasi-affine non-singular surface which do not admit a flat connection. However, to the best of our knowledge there is no known example of such a line bundle. In this article we give several explicit examples of line bundles on certain non-singular, quasi-affine surfaces that cannot be equipped with a flat connection.

On s’attend à ce qu’il existe des fibrés en droites sur une surface non-singulière quasi-affine qui n’admettent pas de connexion plate mais, à notre connaissance, aucun exemple d’un tel fibré n’est connu. Dans cet article, nous en donnons plusieurs exemples explicites.

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Accepté le :
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DOI : 10.5802/crmath.459
Classification : 14B05, 13C14

Dan, Ananyo 1 ; Romano-Velázquez, Agustín 2, 3

1 School of Mathematics and Statistics, University of Sheffield, Hicks building, Hounsfield Road, S3 7RH, UK
2 Alfréd Rényi Institute Of Mathematics, Hungarian Academy Of Sciences, Reáltanoda Utca 13-15, H-1053, Budapest, Hungary
3 Universidad Nacional Autónoma de México Avenida Universidad s/n, Colonia Lomas de Chamilpa CP 62210, Cuernavaca, Morelos Mexico
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {Examples of non-flat bundles of rank one},
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     pages = {965--968},
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Dan, Ananyo; Romano-Velázquez, Agustín. Examples of non-flat bundles of rank one. Comptes Rendus. Mathématique, Tome 361 (2023) no. G6, pp. 965-968. doi: 10.5802/crmath.459

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