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| HAL : hal-00713400, version 3 |
| arXiv : 1207.0208 |
| Fiche détaillée |  Récupérer au format |
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| Versions disponibles : | v1 (01-07-2012) | v2 (01-07-2012) | v3 (02-05-2013) |
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| Polyhedral Divisors, Dedekind Domains and Algebraic Function Fields |
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| Kevin Langlois 1 |
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| (30/06/2012) |
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| We show that the presentation of affine $\mathbb{T}$-varieties of complexity one in terms of polyhedral divisor of Altmann-Hausen holds over an arbitrary field. We describe also a class of multigraded algebras over Dedekind domains. We study how the algebra associated to a polyhedral divisor changes when we extend the scalars. As another application, we provide a combinatorial description of affine $\mathbf{G}$-varieties of complexity one over a field, where $\mathbf{G}$ is a (non-nescessary split) torus, by using elementary facts on Galois descent. This class of affine $\mathbf{G}$-varieties are described via a new combinatorial object, which we call (Galois) invariant polyhedral divisor. |
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| 1 : | Institut Fourier (IF) |
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CNRS : UMR5582 – Université Joseph Fourier - Grenoble I |
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| Domaine | : | Mathématiques/Géométrie algébrique |
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| multigraded ring – polyhedral divisor – algebraic torus action. |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00713400, version 3 | |
| http://hal.archives-ouvertes.fr/hal-00713400 | |
| oai:hal.archives-ouvertes.fr:hal-00713400 | |
| Contributeur : Kevin Langlois | |
| Soumis le : Jeudi 2 Mai 2013, 15:05:29 | |
| Dernière modification le : Jeudi 2 Mai 2013, 22:08:30 | |
