Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Non-hyperbolic complex space with a hyperbolic normalization


Authors: Shulim Kaliman and Mikhail Zaidenberg
Journal: Proc. Amer. Math. Soc. 129 (2001), 1391-1393
MSC (2000): Primary 32H15, 32H20
DOI: https://doi.org/10.1090/S0002-9939-00-05711-7
Published electronically: October 20, 2000
MathSciNet review: 1814164
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We construct an example of a non-hyperbolic singular projective surface $X$ whose normalization $V$ is the square of a genus 3 curve $C$and hence, hyperbolic.


References [Enhancements On Off] (What's this?)

  • 1. A. Grothendieck, Le groupe de Brauer. Dix exposés sur la cohomologie des schémas, 46-65 Mason and Cie, Paris, North-Holland Publ. Co., Amsterdam, 1968. MR 39:5586a
  • 2. Sh. Kobayashi, Hyperbolic manifolds and holomorphic mappings. Marcel Dekker, Inc., New York, 1970. MR 43:3503
  • 3. M.H. Kwack, Generalization of the big Picard theorem. Ann. Math. 90 (1969), 9-22. MR 39:4445
  • 4. B. Moishezon, Complex surfaces and connected sums of complex projective planes. Lect. Notes in Math. 603. Springer, Berlin, 1977. MR 58:10931
  • 5. B. Shiffman and M. Zaidenberg, Two classes of hyperbolic surfaces in $\mathbb{P}^3$. International J. Math. 11:1, 2000 (to appear); preprint MPI-1998-129, 33p., http://www.mpim-bonn.mpg.de/.
  • 6. M. Zaidenberg, Stability of hyperbolic embeddedness and construction of examples. Math. USSR Sbornik 135 (1988), 361-372, 415. MR 89f:32047

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 32H15, 32H20

Retrieve articles in all journals with MSC (2000): 32H15, 32H20


Additional Information

Shulim Kaliman
Affiliation: Department of Mathematics and Computer Science, University of Miami, Coral Gables, Florida 33124
Email: kaliman@cs.miami.edu

Mikhail Zaidenberg
Affiliation: Université Grenoble I, Institut Fourier, UMR 5582 CNRS-UJF, BP 74, 38402 St. Martin d’Hères cédex, France
Email: zaidenbe@ujf-grenoble.fr

DOI: https://doi.org/10.1090/S0002-9939-00-05711-7
Received by editor(s): July 30, 1999
Published electronically: October 20, 2000
Communicated by: Steven R. Bell
Article copyright: © Copyright 2000 American Mathematical Society

American Mathematical Society