Real Algebraic and Analytic Geometry

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262. János Kollár, Frédéric Mangolte:
Cremona transformations and diffeomorphisms of surfaces.

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Submission: 2008, October 28.

Abstract:
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.

Full text, 17p.: pdf 778k.


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