Normal subgroups in the Cremona group

Details Normal subgroups in the Cremona group Normal subgroups in the Cremona group

2010-07-06

arxiv.org/abs/1007.0895v1

Mathematics

Algebraic Geometry

53 pages

Scientific paper

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 which generate
non trivial normal subgroups.

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