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arXiv · 1007.0895

Normal subgroups in the Cremona group (long version)

Serge Cantat·Stéphane Lamy
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Abstract

Let k be an algebraically closed field. We show that the Cremona group of all birational transformations of the projective plane P^2 over k is not a simple group. The strategy makes use of hyperbolic geometry, geometric group theory, and algebraic geometry to produce elements in the Cremona group that generate non trivial normal subgroups.

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Serge Cantat, Stéphane Lamy. 2010-07-06. Normal subgroups in the Cremona group (long version). https://doi.org/10.1007/s11511-013-0090-1

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