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Compact complex manifolds with the DOP and other properties

Published online by Cambridge University Press:  12 March 2014

Anand Pillay  and
Thomas Scanlon
Anand Pillay
Affiliation:
Department of Mathematics, University of Illinois, at Urbana-Champaign, Altgeld Hall, 1409 W. Green St., Urbana, Illinois 61801, USA, E-mail: [email protected]
Thomas Scanlon
Affiliation:
Department of Mathematics, University of California, Berkeley, Berkeley, California 94709, USA, E-mail: [email protected]
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Abstract

We point out that a certain complex compact manifold constructed by Lieberman has the dimensional order property, and has U-rank different from Morley rank. We also give a sufficient condition for a Kähler manifold to be totally degenerate (that is, to be an indiscernible set, in its canonical language) and point out that there are K3 surfaces which satisfy these conditions.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 67 , Issue 2 , June 2002 , pp. 737 - 743
Copyright
Copyright © Association for Symbolic Logic 2002

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References

REFERENCES

[1]Beauville, A., Some remarks on Kähler manifolds with c1 = 0, Classification of algebraic and analytic manifolds (Ueno, K., editor), Progress in Mathematics, vol. 39, Birkhäuser, 1983.Google Scholar
[2]Campana, F., Exemples de sous-espaces maximaux isoles de codimension 2 d'un espace analytique compact, Institut Elie Cartan 6, Univ. Nancy, 1982.Google Scholar
[3]Fischer, G. and Forster, O., Ein Endlichkeit Satz für Hyperflüchen auf kompakten complexen Raümen, Journal für die Reine und Angewandte Mathematik, vol. 306 (1979), pp. 88–93.Google Scholar
[4]Hrushovski, E. and Scanlon, T., Lascar and Morley ranks differ in differentially closed fields, this Journal, vol. 64 (1999), pp. 1280–1285.Google Scholar
[5]Hrushovski, E. and Sokolovic, Z., Minimal sets in differentially closed fields, to appear.Google Scholar
[6]Hrushovski, E. and Zilber, B., Zariski geometries, Bulletin of the American Mathematical Society, vol. 28 (1993), pp. 315–322.CrossRefGoogle Scholar
[7]Hrushovski, E. and Zilber, B., Zariski geometries, Journal of the American Mathematical Society, vol. 9 (1996), pp. 1–56.CrossRefGoogle Scholar
[8]Lieberman, D., Compactness of the Chow scheme: applications to automorphisms and deformations of Kühler manifolds, Seminaire f. norguet, Lecture Notes in Mathematics, vol. 670, Springer-Verlag, 1978.Google Scholar
[9]Moosa, R., Remarks on saturated complex spaces, preprint. 2001.Google Scholar
[10]Pillay, A., Some model theory of compact complex spaces, Contemporary Mathematics, vol. 270, American Mathematical Society, 2000.Google Scholar
[11]Pillay, A., Differential algebraic groups and the number of countable differentially closed fields, Model theory of fields (Messmer, M.Marker, D. and Pillay, A., editors), Lecture Notes in Logic, Asl-A. K. Peters, 2001, corrected and revised edition.Google Scholar
[12]Pillay, A. and Scanlon, T., Meromorphic groups, submitted.Google Scholar
[13]Shelah, S., Classification theory, 2nd ed., North-Holland, 1990.Google Scholar
[14]Wagner, Frank, Fields of finite Morley rank, to appear in this Journal.Google Scholar
[15]Zilber, B., Model theory and algebraic geometry, Proceedings of 10th Easter conference at Berlin, 1993.Google Scholar