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
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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.
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BPV W. Barth; C. Peters and A. Van de Ven, Compact complex surfaces, Springer-Verlag, 1984.
Catanese F. Catanese, On the Moduli Spaces of Surfaces of General Type, Journal of Differential Geometry 19 (1984), 483-515.
Ghys E. 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.
GB X. Gomez-Mont and L. Ortiz-Bobadilla, Sistemas Dinamicos Holomorfos en Superficies, Sociedad Matematica Mexicana, 1989.
Hart R. Hartshorne, Ample subvarieties of algebraic varieties, Lecture Notes in Mathematics, Vol. 156, Springer (1970).
Sebastiani M. Sebastiani, Notes from the Analytic Geometry Seminar at UFRGS, 2003.
Totaro B. Totaro, The topology of smooth divisors and the arithmetic of abelian varieties, Michigan Mathematical Journal, 48 (2000) 611-624.
Ueda T. 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.
Ueno K. Ueno, Classification theory of algebraic varieties and compact complex spaces, Lecture Notes in Mathematics, Vol. 439. Springer-Verlag, 1975.
Vistoli A. Vistoli, Letter to S. Kleiman, 2003.
1 F. Bosio; L. Meersseman, Real quadrics in $\mathbb C^n$, complex manifolds and convex polytopes, preprint, 2004.
2 S. López de Medrano; A. Verjovsky, A new family of complex, compact, non symplectic manifolds, Bol. Soc. Mat. Bra. 28 (2), 253–269, 1997 .
3 L. Meersseman, A new geometric construction of compact complex manifolds in any dimension, Math. Ann. 317, 79–115, 2000.
Additional Information
Jorge Vitório Pereira
Affiliation:
I.R.M.A.R. - Université de Rennes I, Campus de Beaulieu, 35042 Rennes Cedex France;
(\textLaurent 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
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
