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Mild manifolds and a non-standard Riemann existence theorem

    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
  • 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.


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