Examples of non-flat bundles of rank one
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,...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2023-09-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.459/ |
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| author | Dan, Ananyo Romano-Velázquez, Agustín |
| author_facet | Dan, Ananyo Romano-Velázquez, Agustín |
| author_sort | Dan, Ananyo |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-a84455441bab4d21a080badfe66411a8 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2023-09-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-a84455441bab4d21a080badfe66411a82025-02-07T11:09:17ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692023-09-01361G696596810.5802/crmath.45910.5802/crmath.459Examples of non-flat bundles of rank oneDan, Ananyo0Romano-Velázquez, Agustín1School of Mathematics and Statistics, University of Sheffield, Hicks building, Hounsfield Road, S3 7RH, UKAlfréd Rényi Institute Of Mathematics, Hungarian Academy Of Sciences, Reáltanoda Utca 13-15, H-1053, Budapest, Hungary; Universidad Nacional Autónoma de México Avenida Universidad s/n, Colonia Lomas de Chamilpa CP 62210, Cuernavaca, Morelos MexicoIt 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.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.459/ |
| spellingShingle | Dan, Ananyo Romano-Velázquez, Agustín Examples of non-flat bundles of rank one Comptes Rendus. Mathématique |
| title | Examples of non-flat bundles of rank one |
| title_full | Examples of non-flat bundles of rank one |
| title_fullStr | Examples of non-flat bundles of rank one |
| title_full_unstemmed | Examples of non-flat bundles of rank one |
| title_short | Examples of non-flat bundles of rank one |
| title_sort | examples of non flat bundles of rank one |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.459/ |
| work_keys_str_mv | AT danananyo examplesofnonflatbundlesofrankone AT romanovelazquezagustin examplesofnonflatbundlesofrankone |