Cremona transformations and diffeomorphisms of surfaces

János Kollár, Frédéric Mangolte

Research output: Contribution to journalArticlepeer-review

16 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)44-61
Number of pages18
JournalAdvances in Mathematics
Issue number1
StatePublished - Sep 10 2009

All Science Journal Classification (ASJC) codes

  • General Mathematics


  • Automorphism group
  • Diffeomorphism group
  • Mapping class group
  • Rational surface
  • Real algebraic surface


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