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Action of the Cremona group on a noncommutative ring |
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| Authors: | Alexandr Usnich |
| Affiliation: | University of Zurich, Institut fuer Mathematik, 190 Winterthurerstrasse, Zurich, Switzerland |
| Abstract: | The Cremona group acts on the field of two independent commutative variables over complex numbers. We provide a noncommutative algebra that is an analog of a noncommutative field of two independent variables and prove that the Cremona group embeds in a group of outer automorphisms of this algebra. We give two proofs of it, the first proof is technical, the second one is conceptual and proceeds through a construction of a birational invariant of an algebraic variety from its bounded derived category of coherent sheaves. |
| Keywords: | Birational invariant Derived categories Triangulated categories dg-Categories Noncommutative algebra Cremona group Coherent sheaves Quiver representations Localization Rational surfaces Blow-ups Toric surfaces |
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