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| HAL : hal-00618025, version 1 |
| arXiv : 1108.6209 |
| Fiche détaillée |  Récupérer au format |
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| Complements of hyperplane sub-bundles in projective space bundles over the projective line |
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| Adrien Dubouloz 1 |
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| (31/08/2011) |
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| We establish that the isomorphy type as an abstract algebraic variety of the complement of an ample hyperplane sub-bundle H of a projective space bundle of rank r-1 over the projective line depends only on the the r-fold self-intersection of H . In particular it depends neither on the ambient bundle nor on a particular ample hyperplane sub-bundle with given r-fold self-intersection. Our proof exploits the unexpected property that every such complement comes equipped with the structure of a non trivial torsor under a vector bundle on the affine line with a double origin. |
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| 1 : | Institut de Mathématiques de Bourgogne (IMB) |
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CNRS : UMR5584 – Université de Bourgogne |
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| Domaine | : | Mathématiques/Géométrie algébrique |
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| hyperplane sub-bundles – affine-linear bundles – Danilov-Gizatullin Theorem. |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00618025, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00618025 | |
| oai:hal.archives-ouvertes.fr:hal-00618025 | |
| Contributeur : Adrien Dubouloz | |
| Soumis le : Mercredi 31 Août 2011, 14:08:55 | |
| Dernière modification le : Mercredi 31 Août 2011, 14:44:21 | |
