Cremona transformations and diffeomorphisms of surfaces

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.
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Submitted on : Monday, October 27, 2008 - 4:48:53 PM
Last modification on : Thursday, January 11, 2018 - 6:12:26 AM
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  • HAL Id : hal-00323333, version 2
  • ARXIV : 0809.3720

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János Kollár, Frédéric Mangolte. Cremona transformations and diffeomorphisms of surfaces. Advances in Mathematics, Elsevier, 2009, 222, pp.44-61. 〈hal-00323333v2〉

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