Skip to main content
MathOverflow

Return to Question

Added \operatorname to Aut and Bir.
Source Link
edit approved Jul 14, 2022 at 19:36
Samuel Adrian Antz
edit approved Jul 14, 2022 at 19:36
Samuel Adrian Antz
  • 345
  • 1
  • 3
  • 12

When does $Aut$\operatorname{Aut}(X)=Bir=\operatorname{Bir}(X)$ hold?

Let $X$ be a projective complex manifold. Under what condition do we have the equality $Aut(X)=Bir(X)$$\operatorname{Aut}(X)=\operatorname{Bir}(X)$? Here $Aut(X)$$\operatorname{Aut}(X)$ denotes the group of holomorphic automorphisms of $X$ and $Bir(X)$$\operatorname{Bir}(X)$ the group of birational morphisms of $X$.

I am interested in the case when $\dim_{\mathbb{C}}X=2,3$. Maybe there are not universal criteria, so I would appreciate your providing me with any examples for which the equality holds.

When does $Aut(X)=Bir(X)$ hold?

Let $X$ be a projective complex manifold. Under what condition do we have the equality $Aut(X)=Bir(X)$? Here $Aut(X)$ denotes the group of holomorphic automorphisms of $X$ and $Bir(X)$ the group of birational morphisms of $X$.

I am interested in the case when $\dim_{\mathbb{C}}X=2,3$. Maybe there are not universal criteria, so I would appreciate your providing me with any examples for which the equality holds.

When does $\operatorname{Aut}(X)=\operatorname{Bir}(X)$ hold?

Let $X$ be a projective complex manifold. Under what condition do we have the equality $\operatorname{Aut}(X)=\operatorname{Bir}(X)$? Here $\operatorname{Aut}(X)$ denotes the group of holomorphic automorphisms of $X$ and $\operatorname{Bir}(X)$ the group of birational morphisms of $X$.

I am interested in the case when $\dim_{\mathbb{C}}X=2,3$. Maybe there are not universal criteria, so I would appreciate your providing me with any examples for which the equality holds.

edited tags
Link
Leo Alonso
Leo Alonso
  • 9.2k
  • 2
  • 43
  • 57
Source Link
Koopa
Koopa
  • 583
  • 4
  • 10

When does $Aut(X)=Bir(X)$ hold?

Let $X$ be a projective complex manifold. Under what condition do we have the equality $Aut(X)=Bir(X)$? Here $Aut(X)$ denotes the group of holomorphic automorphisms of $X$ and $Bir(X)$ the group of birational morphisms of $X$.

I am interested in the case when $\dim_{\mathbb{C}}X=2,3$. Maybe there are not universal criteria, so I would appreciate your providing me with any examples for which the equality holds.