Real Algebraic and Analytic Geometry
Submission: 2008, October 28.
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.
Mathematics Subject Classification (2000): 14E07, 14P25, 57M20.
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