A nonstandard Riemann existence theorem

Moosa, Rahim

doi:10.1090/S0002-9947-04-03559-7

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

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.