CORDIS Project
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This project investigates the automorphisms of three-dimensional complex space, focusing on the application of Mori theory to understand birational maps. It aims to provide a more conceptual framework for studying these complex transformations, moving beyond previous intricate calculations.
In contrast with the 2-dimensional case, the study of automorphisms of C³ is still in its early beginnings.
The most striking recent result is probably the proof by Shestakov and Umirbaev that a large class of automorphisms of C³ is non tame.
Unfortunately their proof is based on tricky calculations and lacks conceptuality.
On the other hand, Mori theory has emerged since the 1980s as the right framework to study birational maps in higher dimension, of which automorphisms of C³ are special cases…
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