Connected algebraic subgroups of groups of birational transformations not contained in a maximal one
We prove that for each $n\ge 2$, there exist a ruled variety $X$ of dimension $n$ and a connected algebraic subgroup of $\mathrm{Bir}(X)$ which is not contained in a maximal one.
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| Format: | Article |
| Language: | English |
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Académie des sciences
2023-01-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.406/ |
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| author | Fong, Pascal Zikas, Sokratis |
| author_facet | Fong, Pascal Zikas, Sokratis |
| author_sort | Fong, Pascal |
| collection | DOAJ |
| description | We prove that for each $n\ge 2$, there exist a ruled variety $X$ of dimension $n$ and a connected algebraic subgroup of $\mathrm{Bir}(X)$ which is not contained in a maximal one. |
| format | Article |
| id | doaj-art-6c91256fff7c46df9effa66f0d8982b4 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-6c91256fff7c46df9effa66f0d8982b42025-02-07T11:06:07ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692023-01-01361G131332210.5802/crmath.40610.5802/crmath.406Connected algebraic subgroups of groups of birational transformations not contained in a maximal oneFong, Pascal0Zikas, Sokratis1Universität Basel, Departement Mathematik und Informatik, Spiegelgasse 1, CH–4051 Basel, SwitzerlandUniversität Basel, Departement Mathematik und Informatik, Spiegelgasse 1, CH–4051 Basel, SwitzerlandWe prove that for each $n\ge 2$, there exist a ruled variety $X$ of dimension $n$ and a connected algebraic subgroup of $\mathrm{Bir}(X)$ which is not contained in a maximal one.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.406/ |
| spellingShingle | Fong, Pascal Zikas, Sokratis Connected algebraic subgroups of groups of birational transformations not contained in a maximal one Comptes Rendus. Mathématique |
| title | Connected algebraic subgroups of groups of birational transformations not contained in a maximal one |
| title_full | Connected algebraic subgroups of groups of birational transformations not contained in a maximal one |
| title_fullStr | Connected algebraic subgroups of groups of birational transformations not contained in a maximal one |
| title_full_unstemmed | Connected algebraic subgroups of groups of birational transformations not contained in a maximal one |
| title_short | Connected algebraic subgroups of groups of birational transformations not contained in a maximal one |
| title_sort | connected algebraic subgroups of groups of birational transformations not contained in a maximal one |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.406/ |
| work_keys_str_mv | AT fongpascal connectedalgebraicsubgroupsofgroupsofbirationaltransformationsnotcontainedinamaximalone AT zikassokratis connectedalgebraicsubgroupsofgroupsofbirationaltransformationsnotcontainedinamaximalone |