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A nonstandard Riemann existence theorem


Author: Rahim Moosa
Translated by:
Journal: Trans. Amer. Math. Soc. 356 (2004), 1781-1797
MSC (2000): Primary 03C60; Secondary 32J99
DOI: https://doi.org/10.1090/S0002-9947-04-03559-7
Published electronically: January 6, 2004
MathSciNet review: 2031041
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Abstract | References | Similar Articles | Additional Information

Abstract: We study elementary extensions of compact complex spaces and deduce that every complete type of dimension $1$ is internal to projective space. This amounts to a nonstandard version of the Riemann Existence Theorem, and answers a question posed by Anand Pillay.


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  • 1. F. Campana.
    Coréduction algébrique d'un espace analytique faiblement Kählérien compact.
    Inventiones Mathematicae, (63):187-223, 1981. MR 84e:32028
  • 2. F. Campana and T. Peternell.
    Cycle spaces.
    In Grauert et al. [6], pages 319-349. MR 96k:32001
  • 3. G. Fischer.
    Complex Analytic Geometry.
    Springer-Verlag, Berlin, 1976. MR 55:3291
  • 4. A. Fujiki.
    On a holomorphic fibre bundle with meromorphic structure.
    Publications of the Research Institute for Mathemtaical Sciences, 19(1):117-134, 1983. MR 84m:32038
  • 5. A. Fujiki.
    On the structure of compact complex manifolds in $\mathcal{C}$.
    In Algebraic Varieties and Analytic Varieties, volume 1 of Advanced Studies in Pure Mathematics, pages 231-302. North-Holland, Amsterdam, 1983. MR 85g:32045b
  • 6. H. Grauert, T. Peternell, and R. Remmert, editors.
    Several Complex Variables VII, volume 74 of Encyclopedia of Mathematical Sciences.
    Springer-Verlag, Berlin, 1994. MR 96k:32001
  • 7. R. Gunning and H. Rossi.
    Analytic functions of several complex variables.
    Prentice-Hall, Edgewood Cliffs, 1965. MR 31:4927
  • 8. W. Hodges.
    Model Theory.
    Cambridge University Press, Cambridge, 1993. MR 94e:03002
  • 9. R. Moosa.
    The model theory of compact complex spaces.
    To appear in the Proceedings of the Logic Colloquium '01 (Vienna).
  • 10. R. Moosa.
    On saturation and the model theory of compact Kähler manifolds.
    Preprint.
  • 11. R. Moosa.
    Contributions to the model theory of fields and compact complex spaces.
    PhD thesis, University of Illinois, Urbana-Champaign, 2001.
  • 12. T. Peternell and R. Remmert.
    Differential calculus, holomorphic maps and linear structures on complex spaces.
    In Grauert et al. [6], pages 97-144. MR 96k:32001
  • 13. A. Pillay.
    Some model theory of compact complex spaces.
    In Workshop on Hilbert's tenth problem: relations with arithmetic and algebraic geometry, volume 270 of Contemporary Mathematics, Amer. Math. Soc., Providence, RI, 2000, pp. 323-338. MR 2001m:03076
  • 14. B. Poizat.
    Groupes stables.
    Nur al-Mantiq wal-Ma'rifah, Villeurbanne, 1987. MR 89b:03056
  • 15. R. Remmert.
    Local theory of complex spaces.
    In Grauert et al. [6], pages 10-96. MR 96k:32001
  • 16. K. Ueno.
    Classification Theory of Algebraic Varieties and Compact Complex Spaces, volume 439 of Lecture Notes in Mathematics.
    Springer-Verlag, Berlin, 1975. MR 58:22062
  • 17. B. Zilber.
    Model theory and algebraic geometry.
    In Proceedings of the 10th Easter Conference on Model Theory, Berlin, 1993.

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Additional Information

Rahim Moosa
Affiliation: The Fields Institute, 222 College Street, Toronto, Ontario, Canada M5T 3J1
Address at time of publication: Massachusetts Institute of Technology, Department of Mathematics, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139-4307
Email: moosa@math.mit.edu

DOI: https://doi.org/10.1090/S0002-9947-04-03559-7
Received by editor(s): July 17, 2002
Published electronically: January 6, 2004
Additional Notes: This work was supported by the Natural Science and Engineering Research Council of Canada
Article copyright: © Copyright 2004 American Mathematical Society

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