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- W4297788789 abstract "We give some properties of the subgroup $G_n(mathbb{C})$ of the group of birational self-maps of $mathbb{P}^n_mathbb{C}$ generated by the standard involution and the group of automorphisms of $mathbb{P}^n_mathbb{C}$. We prove that there is no nontrivial finite-dimensional linear representation of $G_n(mathbb{C})$. We also establish that $G_n(mathbb{C})$ is perfect, and that $G_n(mathbb{C})$ equipped with the Zariski topology is simple. Furthermore if $varphi$ is an automorphism of $mathrm{Bir}(mathbb{P}^n_mathbb{C})$, then up to birational conjugacy, and up to the action of a field automorphism $varphi_{vert G_n(mathbb{C})}$ is trivial." @default.
- W4297788789 created "2022-10-01" @default.
- W4297788789 creator A5048008207 @default.
- W4297788789 date "2014-03-03" @default.
- W4297788789 modified "2023-10-17" @default.
- W4297788789 title "Some properties of the group of birational maps generated by the automorphisms of $mathbb{P}^n_mathbb{C}$ and the standard involution" @default.
- W4297788789 doi "https://doi.org/10.48550/arxiv.1403.0346" @default.
- W4297788789 hasPublicationYear "2014" @default.
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