Automorphisms of unstable ${\mathbb P}^1$-bundles
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866911903174885376 |
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| author | Kollár, János |
| author_facet | Kollár, János |
| contents | Let $P\to X$ be a ${\mathbb P}^1$-bundle over a variety $X$. The aim of this note is to understand all connected, algebraic groups $$ \operatorname{Aut}^\circ(P)\subset G\subset \operatorname{Bir}( X\times {\mathbb P}^1). $$ We get a quite complete answer if $\operatorname{Aut}^\circ(X)$ is a maximal, connected, algebraic subgroup of $\operatorname{Bir}(X)$, and $P$ is sufficiently unstable.
This gives examples of connected, algebraic subgroups of $\operatorname{Bir}({\mathbb P}^4)$ that are not contained in any maximal one.
Version 2: references updated. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_18201 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Automorphisms of unstable ${\mathbb P}^1$-bundles Kollár, János Algebraic Geometry Let $P\to X$ be a ${\mathbb P}^1$-bundle over a variety $X$. The aim of this note is to understand all connected, algebraic groups $$ \operatorname{Aut}^\circ(P)\subset G\subset \operatorname{Bir}( X\times {\mathbb P}^1). $$ We get a quite complete answer if $\operatorname{Aut}^\circ(X)$ is a maximal, connected, algebraic subgroup of $\operatorname{Bir}(X)$, and $P$ is sufficiently unstable. This gives examples of connected, algebraic subgroups of $\operatorname{Bir}({\mathbb P}^4)$ that are not contained in any maximal one. Version 2: references updated. |
| title | Automorphisms of unstable ${\mathbb P}^1$-bundles |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2405.18201 |