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| HAL : hal-00323517, version 1 |
| arXiv : math/0511063 |
| Fiche détaillée |  Récupérer au format |
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| Affine algebraic geometry, T. Hibi (Ed.) (2007) 107-147 |
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| Birational transformations of weighted graphs |
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| Hubert Flenner 1Shulim Kaliman 2 |
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| (2007) |
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| We introduce the notion of a standard weighted graph and show that every weighted graph has an essentially unique standard model. Moreover we classify birational transformations between such models. Our central result shows that these are composed of elementary transformations. The latter ones are defined similarly to the well known elementary transformations of ruled surfaces. In a forthcoming paper, we apply these results in the geometric setup to obtain standard equivariant completions of affine surfaces with an action of certain algebraic groups. We show that these completions are unique up to equivariant elementary transformations. |
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| 1 : | Fakultät für Mathematik (Fakultät für Mathematik) |
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Ruhr-Universität Bochum |
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| 2 : | Department of Mathematics [Miami] |
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University of Miami |
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| 3 : | Institut Fourier (IF) |
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CNRS : UMR5582 – Université Joseph Fourier - Grenoble I |
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| Domaine | : | Mathématiques/Géométrie algébrique Mathématiques/Combinatoire |
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| Weighted graph – standard model – minimal model – birational transformation – elementary transformation |
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| Lien vers le texte intégral : |
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| http://fr.arXiv.org/abs/math/0511063 |
| hal-00323517, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00323517 | |
| oai:hal.archives-ouvertes.fr:hal-00323517 | |
| Contributeur : Mikhail Zaidenberg | |
| Soumis le : Lundi 22 Septembre 2008, 13:48:24 | |
| Dernière modification le : Jeudi 18 Décembre 2008, 15:42:07 | |
