|Universiteit Faculteit FNWI English version||24 april 2003, e-mail|
Woensdag 14 mei 2003
AbstractLet F: Cn → Cn be a polynomial map. Then F is called invertible if there exists a polynomial map G: Cn → Cn such that G ° F = 1Cn. Examples of such maps are the elementary polynomial maps i.e. maps of the form
Tame Generators Problem Is every invertible polynomial map tame i.e. a finite composition of elementary polynomial maps?
For n = 2 the answer is yes (Jung 1942).
In a recent paper (to be published in Journal of the AMS 2003/2004) Shestakov and Umirbaev proved Nagata's conjecture, thereby showing the existence of wild automorphisms in dimension 3!
In the talk I will sketch the main ideas of their proof.