Cremona transformations and diffeomorphisms of surfaces

Details Cremona transformations and diffeomorphisms of surfaces Cremona transformations and diffeomorphisms of surfaces

2008-09-22

arxiv.org/abs/0809.3720v2

Advances in Mathematics 222 (2009) 44-61

Mathematics

Algebraic Geometry

17 pages, 11 figures, shorter proofs and improvement of the results

Scientific paper

We show that the action of Cremona transformations on the real points of
quadrics exhibits the full complexity of the diffeomorphisms of the sphere, the
torus, and of all non-orientable surfaces. The main result says that if X is
rational, then Aut(X), the group of algebraic automorphisms, is dense in
Diff(X), the group of self-diffeomorphisms of X.

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