Mild manifolds and a non-standard Riemann existence theorem

• Ya'acov Peterzil ^[1] ; Sergei Starchenko ^[2]
  1. [1] University of Haifa

     University of Haifa

     Israel

     
  2. [2] University of Notre Dame

     University of Notre Dame

     Township of Portage, Estados Unidos

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 14, Nº. 2, 2009, págs. 275-298
• Idioma: inglés
• Enlaces
  • Texto completo (pdf)
• Resumen

  • Let R be an o-minimal expansion of a real closed field R, and K be the algebraic closure of R. In earlier papers we investigated the notions of R -definable K-holomorphic maps, K-analytic manifolds and their K-analytic subsets. We call such a K-manifold mild if it eliminates quantifers after endowing it with all it K-analytic subsets. Examples are compact complex manifolds and non-singular algebraic curves over K.

    We examine here basic properties of mild manifolds and prove that when a mild manifold M is strongly minimal and not locally modular then it is biholomorphic to a non-singular algebraic curve over K.