Birational transformations

1952 ◽  
Vol 48 (3) ◽  
pp. 383-391
Author(s):  
T. G. Room

This paper falls into three sections: (1) a system of birational transformations of the projective plane determined by plane cubic curves of a pencil (with nine associated base points), (2) some one-many transformations determined by the pencil, and (3) a system of birational transformations of three-dimensional projective space determined by the elliptic quartic curves through eight associated points (base of a net of quadric surfaces).


2008 ◽  
Vol 139 (1) ◽  
pp. 57-73 ◽  
Author(s):  
Jérémy Blanc ◽  
Ivan Pan ◽  
Thierry Vust

Author(s):  
Serge Cantat ◽  
Vincent Guirardel ◽  
Anne Lonjou

Abstract Consider an algebraically closed field ${\textbf{k}}$, and let $\textsf{Cr}_2({\textbf{k}})$ be the Cremona group of all birational transformations of the projective plane over ${\textbf{k}}$. We characterize infinite order elements $g\in \textsf{Cr}_2({\textbf{k}})$ having a power $g^n$, $n\neq 0$, generating a proper normal subgroup of $\textsf{Cr}_2({\textbf{k}})$.


2016 ◽  
Vol 289 ◽  
pp. 567-602 ◽  
Author(s):  
Alberto Alzati ◽  
José Carlos Sierra

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