Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 

 

Fibrations, divisors and transcendental leaves


Author: Jorge Vitório Pereira; with an Appendix by Laurent Meersseman
Journal: J. Algebraic Geom. 15 (2006), 87-110
DOI: https://doi.org/10.1090/S1056-3911-05-00417-0
Published electronically: September 7, 2005
MathSciNet review: 2177196
Full-text PDF

Abstract | References | Additional Information

Abstract: We use flat divisors, and canonically associated singular holomorphic foliations, to investigate some of the geometry of compact complex manifolds. The paper is mainly concerned with three distinct problems: the existence of fibrations, the topology of smooth hypersurfaces, and the topological closure of transcendental leaves of foliations.


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

  • 1. W. Barth, C. Peters, and A. Van de Ven, Compact complex surfaces, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 4, Springer-Verlag, Berlin, 1984. MR 749574
  • 2. F. Catanese, On the moduli spaces of surfaces of general type, J. Differential Geom. 19 (1984), no. 2, 483–515. MR 755236
  • 3. Étienne Ghys, À propos d’un théorème de J.-P. Jouanolou concernant les feuilles fermées des feuilletages holomorphes, Rend. Circ. Mat. Palermo (2) 49 (2000), no. 1, 175–180 (French, with English summary). MR 1753461, https://doi.org/10.1007/BF02904228
  • 4. X. Gómez-Mont and L. Ortíz-Bobadilla, Sistemas dinámicos holomorfos en superficies, Aportaciones Matemáticas: Notas de Investigación [Mathematical Contributions: Research Notes], vol. 3, Sociedad Matemática Mexicana, México, 1989 (Spanish). MR 1304495
  • 5. Robin Hartshorne, Ample subvarieties of algebraic varieties, Lecture Notes in Mathematics, Vol. 156, Springer-Verlag, Berlin-New York, 1970. Notes written in collaboration with C. Musili. MR 0282977
  • 6. M. Sebastiani, Notes from the Analytic Geometry Seminar at UFRGS, 2003.
  • 7. Burt Totaro, The topology of smooth divisors and the arithmetic of abelian varieties, Michigan Math. J. 48 (2000), 611–624. Dedicated to William Fulton on the occasion of his 60th birthday. MR 1786508, https://doi.org/10.1307/mmj/1030132736
  • 8. Tetsuo Ueda, On the neighborhood of a compact complex curve with topologically trivial normal bundle, J. Math. Kyoto Univ. 22 (1982/83), no. 4, 583–607. MR 685520
  • 9. Kenji Ueno, Classification theory of algebraic varieties and compact complex spaces, Lecture Notes in Mathematics, Vol. 439, Springer-Verlag, Berlin-New York, 1975. Notes written in collaboration with P. Cherenack. MR 0506253
  • 10. A. Vistoli, Letter to S. Kleiman, 2003.


Additional Information

Jorge Vitório Pereira
Affiliation: I.R.M.A.R. - Université de Rennes I, Campus de Beaulieu, 35042 Rennes Cedex France; (Laurent Meersseman) I.R.M.A.R. - Université de Rennes I, Campus de Beaulieu, 35042 Rennes Cedex France
Address at time of publication: IMPA - Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, 22460-320 Rio de Janeiro, Brasil
Email: jvp@impa.br

DOI: https://doi.org/10.1090/S1056-3911-05-00417-0
Received by editor(s): June 29, 2004
Received by editor(s) in revised form: September 7, 2004, March 24, 2005, and April 13, 2005
Published electronically: September 7, 2005
Additional Notes: The author was partially supported by PROFIX/CNPq and CNRS

Journal of Algebraic Geometry
The Journal of Algebraic Geometry
is sponsored by the Department of Mathematical Sciences
of Tsinghua University
and is distributed by the American Mathematical Society
for University Press, Inc.
Online ISSN 1534-7486; Print ISSN 1056-3911
© 2017 University Press, Inc.
Comments: jag-query@ams.org
AMS Website