Skip to main content
MathOverflow

Return to Question

deleted 56 characters in body
Source Link
Soby
Soby
  • 157
  • 8

In this paper: https://perso.univ-rennes1.fr/serge.cantat/Articles/nsgc-acta-c.pdf the authors said that their result that $\text{Bir}(\mathbb{P}_\mathbb{C}^2)$ is not simplearticle 'directly implied' that $\text{Bir}(\mathbb{P}_\mathbb{R}^2)$ is not simple as well. How can we infer the non-simplicity of $\text{Bir}(\mathbb{P}_\mathbb{R}^2)$ just from the fact that $\text{Bir}(\mathbb{P}_\mathbb{C}^2)$ is not simple?

I am thinking of choosing a proper normal subgroup, say $N$, of $\text{Bir}(\mathbb{P}_\mathbb{C}^2)$ and intersecting it with $\text{Bir}(\mathbb{P}_\mathbb{R}^2)$. But there is no guarantee that $\text{Bir}(\mathbb{P}_\mathbb{R}^2)\cap N$ is non-trivial. How does one choose an $N$ s.t $\text{Bir}(\mathbb{P}_\mathbb{R}^2)\cap N$ is nontrivial?

In this paper: https://perso.univ-rennes1.fr/serge.cantat/Articles/nsgc-acta-c.pdf the authors said that their result that $\text{Bir}(\mathbb{P}_\mathbb{C}^2)$ is not simple 'directly implied' that $\text{Bir}(\mathbb{P}_\mathbb{R}^2)$ is not simple as well. How can we infer the non-simplicity of $\text{Bir}(\mathbb{P}_\mathbb{R}^2)$ just from the fact that $\text{Bir}(\mathbb{P}_\mathbb{C}^2)$ is not simple?

I am thinking of choosing a proper normal subgroup, say $N$, of $\text{Bir}(\mathbb{P}_\mathbb{C}^2)$ and intersecting it with $\text{Bir}(\mathbb{P}_\mathbb{R}^2)$. But there is no guarantee that $\text{Bir}(\mathbb{P}_\mathbb{R}^2)\cap N$ is non-trivial. How does one choose an $N$ s.t $\text{Bir}(\mathbb{P}_\mathbb{R}^2)\cap N$ is nontrivial?

In this paper: https://perso.univ-rennes1.fr/serge.cantat/Articles/nsgc-acta-c.pdf the authors said that their article 'directly implied' that $\text{Bir}(\mathbb{P}_\mathbb{R}^2)$ is not simple as well. How can we infer the non-simplicity of $\text{Bir}(\mathbb{P}_\mathbb{R}^2)$ just from the fact that $\text{Bir}(\mathbb{P}_\mathbb{C}^2)$ is not simple?

I am thinking of choosing a proper normal subgroup, say $N$, of $\text{Bir}(\mathbb{P}_\mathbb{C}^2)$ and intersecting it with $\text{Bir}(\mathbb{P}_\mathbb{R}^2)$. But there is no guarantee that $\text{Bir}(\mathbb{P}_\mathbb{R}^2)\cap N$ is non-trivial. How does one choose an $N$ s.t $\text{Bir}(\mathbb{P}_\mathbb{R}^2)\cap N$ is nontrivial?

added 2 characters in body
Source Link
ThiKu
ThiKu
  • 10.4k
  • 2
  • 38
  • 64

In this paper: https://perso.univ-rennes1.fr/serge.cantat/Articles/nsgc-acta-c.pdf the authors said that their result that $\text{Bir}(\mathbb{P}_\mathbb{C}^2)$ is not simesimple 'directly implied' that $\text{Bir}(\mathbb{P}_\mathbb{R}^2)$ is not simple as well. How can we infer the non-simplicity of $\text{Bir}(\mathbb{P}_\mathbb{R}^2)$ just from the fact that $\text{Bir}(\mathbb{P}_\mathbb{C}^2)$ is not simple?

I am thinking of choosing a proper normal subgroup, say $N$, of $\text{Bir}(\mathbb{P}_\mathbb{C}^2)$ and intersecting it with $\text{Bir}(\mathbb{P}_\mathbb{R}^2)$. But there is no guarantee that $\text{Bir}(\mathbb{P}_\mathbb{N}^2)\cap N$$\text{Bir}(\mathbb{P}_\mathbb{R}^2)\cap N$ is non-trivial. How does one choose an $N$ s.t $\text{Bir}(\mathbb{P}_\mathbb{N}^2)\cap N$$\text{Bir}(\mathbb{P}_\mathbb{R}^2)\cap N$ is nontrivial?

In this paper: https://perso.univ-rennes1.fr/serge.cantat/Articles/nsgc-acta-c.pdf the authors said that their result that $\text{Bir}(\mathbb{P}_\mathbb{C}^2)$ is not sime 'directly implied' that $\text{Bir}(\mathbb{P}_\mathbb{R}^2)$ is not simple as well. How can we infer the non-simplicity of $\text{Bir}(\mathbb{P}_\mathbb{R}^2)$ just from the fact that $\text{Bir}(\mathbb{P}_\mathbb{C}^2)$ is not simple?

I am thinking of choosing a proper normal subgroup, say $N$, of $\text{Bir}(\mathbb{P}_\mathbb{C}^2)$ and intersecting it with $\text{Bir}(\mathbb{P}_\mathbb{R}^2)$. But there is no guarantee that $\text{Bir}(\mathbb{P}_\mathbb{N}^2)\cap N$ is non-trivial. How does one choose an $N$ s.t $\text{Bir}(\mathbb{P}_\mathbb{N}^2)\cap N$ is nontrivial?

In this paper: https://perso.univ-rennes1.fr/serge.cantat/Articles/nsgc-acta-c.pdf the authors said that their result that $\text{Bir}(\mathbb{P}_\mathbb{C}^2)$ is not simple 'directly implied' that $\text{Bir}(\mathbb{P}_\mathbb{R}^2)$ is not simple as well. How can we infer the non-simplicity of $\text{Bir}(\mathbb{P}_\mathbb{R}^2)$ just from the fact that $\text{Bir}(\mathbb{P}_\mathbb{C}^2)$ is not simple?

I am thinking of choosing a proper normal subgroup, say $N$, of $\text{Bir}(\mathbb{P}_\mathbb{C}^2)$ and intersecting it with $\text{Bir}(\mathbb{P}_\mathbb{R}^2)$. But there is no guarantee that $\text{Bir}(\mathbb{P}_\mathbb{R}^2)\cap N$ is non-trivial. How does one choose an $N$ s.t $\text{Bir}(\mathbb{P}_\mathbb{R}^2)\cap N$ is nontrivial?

Source Link
Soby
Soby
  • 157
  • 8

Non- simplicity of $\text{Bir}(\mathbb{P}_\mathbb{R}^2)$

In this paper: https://perso.univ-rennes1.fr/serge.cantat/Articles/nsgc-acta-c.pdf the authors said that their result that $\text{Bir}(\mathbb{P}_\mathbb{C}^2)$ is not sime 'directly implied' that $\text{Bir}(\mathbb{P}_\mathbb{R}^2)$ is not simple as well. How can we infer the non-simplicity of $\text{Bir}(\mathbb{P}_\mathbb{R}^2)$ just from the fact that $\text{Bir}(\mathbb{P}_\mathbb{C}^2)$ is not simple?

I am thinking of choosing a proper normal subgroup, say $N$, of $\text{Bir}(\mathbb{P}_\mathbb{C}^2)$ and intersecting it with $\text{Bir}(\mathbb{P}_\mathbb{R}^2)$. But there is no guarantee that $\text{Bir}(\mathbb{P}_\mathbb{N}^2)\cap N$ is non-trivial. How does one choose an $N$ s.t $\text{Bir}(\mathbb{P}_\mathbb{N}^2)\cap N$ is nontrivial?