Cremona transformations and diffeomorphisms of surfaces

János Kollár, Frédéric Mangolte

Research output: Contribution to journalArticle

12 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)44-61
Number of pages18
JournalAdvances in Mathematics
Volume222
Issue number1
DOIs
StatePublished - Sep 10 2009

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

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

Fingerprint Dive into the research topics of 'Cremona transformations and diffeomorphisms of surfaces'. Together they form a unique fingerprint.

  • Cite this