Comptes Rendus
Analyse et géométrie complexes
Examples of non-flat bundles of rank one
[Exemples de fibrés en droites qui ne sont pas plats]
Ananyo Dan1  ; Agustín Romano-Velázquez2, 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, Volume 361 (2023), pp. 965-968.

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.

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.

Reçu le :
Accepté le :
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DOI : 10.5802/crmath.459
Classification : 14B05, 13C14
Ananyo Dan 1 ; Agustín Romano-Velázquez 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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Ananyo Dan; Agustín Romano-Velázquez. Examples of non-flat bundles of rank one. Comptes Rendus. Mathématique, Volume 361 (2023), pp. 965-968. doi : 10.5802/crmath.459. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.459/

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