Hostname: page-component-76fb5796d-r6qrq Total loading time: 0 Render date: 2024-04-27T05:23:16.676Z Has data issue: false hasContentIssue false
  • English
  • Français

Strongly minimal groups in the theory of compact complex spaces

Published online by Cambridge University Press:  12 March 2014

Matthias Aschenbrenner ,
Rahim Moosa  and
Thomas Scanlon
Matthias Aschenbrenner
Affiliation:
University of Illinoisat Chicago, Department of Mathematics. Statistics, and Computer Science, 851 S. Morgan St. (M/C 249)
Rahim Moosa
Affiliation:
University of Waterloo, Department of Pure Mathematics, 200 University Avenue West, Waterloo
Thomas Scanlon
Affiliation:
University of California, Berkeley, Department of Mathematics
Get access Rights & Permissions [Opens in a new window]

Abstract

We characterise strongly minimal groups interpretable in elementary extensions of compact complex analytic spaces.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 71 , Issue 2 , June 2006 , pp. 529 - 552
Copyright
Copyright © Association for Symbolic Logic 2006

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Bouscaren, E., Model theoretic versions of Weil's theorem on pregroups, The Model Theory of Groups (Nesin, A. and Pillay, A., editors). Notre Dame Mathematical Lectures, vol. 11, University of Notre Dame Press, Notre Dame, 1989, pp. 177–185.Google Scholar
[2]Douady, A., Le problème des modules pour les sous-espaces analytiques compacts d'un espace analytique donné, Annates de l'Institut Fourier, vol. 16 (1966), pp. 1–95. Université de Grenoble.CrossRefGoogle Scholar
[3]van den Dries, L., Tame Topology and O-Minimal Structures, London Mathematical Society Lecture Note Series, vol. 248, Cambridge University Press, 1998.CrossRefGoogle Scholar
[4]Fujiki, A., On automorphism groups of compact Kähler manifolds, Inventiones Mathematicae, vol. 44 (1978), no. 3. pp. 225–258.CrossRefGoogle Scholar
[5]Fujiki, A., Closedness of the Douady spaces of compact Kähler spaces, Publications of the Research Institute for Mathematical Sciences, Kyoto University, vol. 14 (1978/1979). no. 1. pp. 1–52.CrossRefGoogle Scholar
[6]Fujiki, A., On the Douady space of a compact complex space in the category , Nagoya Mathematical Journal, vol. 85 (1982), pp. 189–211.CrossRefGoogle Scholar
[7]Fujiki, A., On a holomorphic fiber bundle with meromorphic structure, Publications of the Research Institute for Mathematical Sciences, Kyoto University, vol. 19 (1983), no. 1, pp. 117–134.CrossRefGoogle Scholar
[8]Grothendieck, A., Techniques de construction en géométric analytique VII. Étude locale des morphisme: éléments de calcul infinitésimal. Séminaire Henri Cartan. 13ième année: 1960/1961. Families d'espaces complexes et fondements de la géométrie analytique. Fasc. 1 et 2: Exp. 1–21. 2iéme édition, corrigée. École Normale Supérieure, Secrétariat mathématique. Paris. 1962.Google Scholar
[9]Johns, J., An open mapping theorem for o-minimal structures, this Journal, vol. 66 (2001), no. 4. pp. 1817–1820.Google Scholar
[10]Moosa, R., Jet spaces in complex analytic geometry: An exposition. E-print available at http://arxiv.org/abs/math.L0/0405563.Google Scholar
[11]Fujiki, A., A nonstandard Riemann existence theorem, Transactions of the American Mathematical Society, vol. 356 (2004), no. 5, pp. 1781–1797.Google Scholar
[12]Fujiki, A., On saturation and the model theory of compact Kähler manifolds, Journal für die reine und angewandte Mathematik, vol. 586 (2005), pp. 1–20.Google Scholar
[13]Peterzil, Y. and Starchenko, S., Expansions of algebraically closed fields in o-minimal structures, Selecta Mathematica, (New series), vol. 7 (2001), no. 3, pp. 409–445.CrossRefGoogle Scholar
[14]Fujiki, A., Expansions of algebraically closed fields. II. Functions of several variables, Journal of Mathematical Logic, vol. 3 (2003). no. 1. pp. 1–35.Google Scholar
[15]Pillay, A. and Scanlon, T., Compact complex manifolds with the DOP and other properties, this Journal, vol. 67 (2002), no. 2, pp. 737–743.Google Scholar
[16]Pillay, A. and Scanlon, T., Meromorphic groups, Transactions of the American Mathematical Society, vol. 355 (2003), no. 10. pp. 3843–3859.CrossRefGoogle Scholar
[17]Pourcin, G., Théorème de Douady au-dessus de S, Annali delta Scuola Normale Superiore di Pisa (3), vol. 23 (1969), pp. 451–459.Google Scholar
[18]Remmert, R.. Local theory of complex spaces, Several Complex Variables VII (Grauert, H., Peternell, T., and Remmert, R., editors). Encyclopedia of Mathematical Sciences, vol. 74. Springer-Verlag, Berlin, 1994, pp. 10–96.CrossRefGoogle Scholar
[19]Scanlon, T., Nonstandard meromorphic groups, Electronic Notes in Theoretical Computer Science, Conference Proceedings of WoLLIC 2005 (Florianópolis, Brazil), to appear.Google Scholar
[20]Schuster, H. W., Zur Theorie der Deformationen kompakter komplexer Räume, Inventiones Mathematicae, vol. 9 (1969/1970), pp. 284–294.CrossRefGoogle Scholar
[21]Zilber, B.. Model theory and algebraic geometry, Proceedings of the 10th Easter Conference on Model Theory, Seminarbericht 93-1, Fachbereich Mathematik. Humboldt Universität, Berlin, 1993, pp. 202–222.Google Scholar