English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We describe the group of birational transformations of a non-trivialSeveri-Brauer surface over a perfect field $K$, proving in particular that ifit contains a point of degree $6$, then it is not generated by elements offinite order as it admits a surjective group homomorphism to $\mathbb{Z}$.  We then use this result to study Mori fibre spaces over the field of complexnumbers, for which the generic fibre is a non-trivial Severi-Brauer surface. Weprove that any group of cardinality at most the one of $\mathbb{C}$ is aquotient of any Cremona group of rank at least $4$. As a consequence, thisgives a negative answer to the question of Dolgachev of whether the Cremonagroups of all ranks are generated by involutions. We also prove that the$3$-torsion of the Cremona group of rank at least $4$ is not countable.

Birational maps of Severi-Brauer surfaces, with applications to Cremona groups of higher rank