Universiteit Faculteit FNWI English version | 24 april 2003, e-mail |

## Woensdag 14 mei 2003
Vanaf half 11 is er koffie en chocola.
## AbstractLetF:
be a polynomial map.
Then C^{n} → C^{n}F is called invertible if there exists a polynomial map
G:
such that C^{n} → C^{n}G ° F = 1.
Examples of such maps are the elementary polynomial maps i.e. maps of the form
_{Cn}_{1}, ... , x_{n}) →
(x_{1} ... , x_{i-1},
λ x_{i} +
a (x_{1}, ... , x_{i-1}, x_{i+1}, ... , x_{n}),
x_{i+1}, ... , x_{n}), λ ε C*.
For
σ: (x,y,z) → ( x - 2(xz + y^{2})y - (xz + y^{2})^{2} z, y + (xz + y^{2}) z, z )
σ is wild i.e. not tame.
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. |