Elements Generating a Proper Normal Subgroup of the Cremona Group. (16th April 2020)

• Record Type: Journal Article
• Authors: Cantat, Serge; Guirardel, Vincent; Lonjou, Anne
• Is Part Of: International mathematics research notices. Volume 2021:Number 10(2021)
• Page Start: 7339
• Page End: 7371
• Publication Date: 2020-04-16
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1093/imrn/rnaa026
• Languages: English
• ISSNs: 1073-7928

Abstract

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 $\textsf{Cr}_2({\textbf{k}})$ .