The Structure of Algebraic Families of Birational Transformations
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913495858020352 |
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| author | Regeta, Andriy Urech, Christian van Santen, Immanuel |
| author_facet | Regeta, Andriy Urech, Christian van Santen, Immanuel |
| contents | We give a description of the algebraic families of birational transformations of an algebraic variety X. As an application, we show that the morphisms to Bir(X) given by algebraic families satisfy a Chevalley type result and a certain fibre-dimension formula. Moreover, we show that the algebraic subgroups of Bir(X) are exactly the closed finite-dimensional subgroups with finitely many components. We also study algebraic families of birational transformations preserving a fibration. This builds on previous work of Blanc-Furter, Hanamura, and Ramanujam. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_06475 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Structure of Algebraic Families of Birational Transformations Regeta, Andriy Urech, Christian van Santen, Immanuel Algebraic Geometry 14E07, 14L30 We give a description of the algebraic families of birational transformations of an algebraic variety X. As an application, we show that the morphisms to Bir(X) given by algebraic families satisfy a Chevalley type result and a certain fibre-dimension formula. Moreover, we show that the algebraic subgroups of Bir(X) are exactly the closed finite-dimensional subgroups with finitely many components. We also study algebraic families of birational transformations preserving a fibration. This builds on previous work of Blanc-Furter, Hanamura, and Ramanujam. |
| title | The Structure of Algebraic Families of Birational Transformations |
| topic | Algebraic Geometry 14E07, 14L30 |
| url | https://arxiv.org/abs/2409.06475 |