Talk:Cremona group

Is this named after John Cremona? A Geek Tragedy 10:25, 2 October 2006 (UTC)

Looks like I'm not the only Wikipedian who scans arXiv/recent for interesting stuff! Melchoir 17:04, 12 October 2006 (UTC)

:Luigi Cremona. Charles Matthews 21:18, 12 October 2006 (UTC)

This article should be on Cremona transformations (which redirects here), with Cremona

groups as a development of the concept. Geometry guy 00:32, 17 May 2007 (UTC)

The section The Cremona group in 2 dimensions begins as follows:

"In two dimensions, Max Noether and Guido Castelnuovo showed that the complex Cremona group is generated by the standard quadratic transformation, along with , though there was some controversy about whether their proofs were correct, and Gizatullin (1983) gave a complete set of relations for these generators."

But nothing is stated about what the "standard quadratic transformation" might be, nor is any link proovided.

I hope someone knowledgeable about this subject can fill in this missing information.

Also: The introductory section contains this sentence:

"The Cremona group is naturally identified with the automorphism group of the field of the rational functions in indeterminates over, or in other words a pure transcendental extension of, with transcendence degree."

But this is a poorly written sentence. What is "in other words" ???