Positivity, vanishing theorems and rigidity of Codimension one Holomorphic Foliations

O. Calvo-Andrade[1]

  • [1] CIMAT: Ap. Postal 402, Guanajuato, 36000, Gto. México

Annales de la faculté des sciences de Toulouse Mathématiques (2009)

  • Volume: 18, Issue: 4, page 811-854
  • ISSN: 0240-2963

Abstract

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It is a known fact that the space of codimension one holomorphic foliations with singularities with a given ‘normal bundle’ has a natural structure of an algebraic variety. The aim of this paper is to consider the problem of the description of its irreducible components. To do this, we are interested in the problem of the existence of an integral factor of a twisted integrable differential 1–form defined on a projective manifold. We are going to do a geometrical analysis of the codimension one foliation associated to this form. The essential point of this paper consists in understanding the role played by a positive condition on some object associated to the foliation.

How to cite

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Calvo-Andrade, O.. "Positivity, vanishing theorems and rigidity of Codimension one Holomorphic Foliations." Annales de la faculté des sciences de Toulouse Mathématiques 18.4 (2009): 811-854. <http://eudml.org/doc/10128>.

@article{Calvo2009,
abstract = {It is a known fact that the space of codimension one holomorphic foliations with singularities with a given ‘normal bundle’ has a natural structure of an algebraic variety. The aim of this paper is to consider the problem of the description of its irreducible components. To do this, we are interested in the problem of the existence of an integral factor of a twisted integrable differential 1–form defined on a projective manifold. We are going to do a geometrical analysis of the codimension one foliation associated to this form. The essential point of this paper consists in understanding the role played by a positive condition on some object associated to the foliation.},
affiliation = {CIMAT: Ap. Postal 402, Guanajuato, 36000, Gto. México},
author = {Calvo-Andrade, O.},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
language = {eng},
month = {10},
number = {4},
pages = {811-854},
publisher = {Université Paul Sabatier, Toulouse},
title = {Positivity, vanishing theorems and rigidity of Codimension one Holomorphic Foliations},
url = {http://eudml.org/doc/10128},
volume = {18},
year = {2009},
}

TY - JOUR
AU - Calvo-Andrade, O.
TI - Positivity, vanishing theorems and rigidity of Codimension one Holomorphic Foliations
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2009/10//
PB - Université Paul Sabatier, Toulouse
VL - 18
IS - 4
SP - 811
EP - 854
AB - It is a known fact that the space of codimension one holomorphic foliations with singularities with a given ‘normal bundle’ has a natural structure of an algebraic variety. The aim of this paper is to consider the problem of the description of its irreducible components. To do this, we are interested in the problem of the existence of an integral factor of a twisted integrable differential 1–form defined on a projective manifold. We are going to do a geometrical analysis of the codimension one foliation associated to this form. The essential point of this paper consists in understanding the role played by a positive condition on some object associated to the foliation.
LA - eng
UR - http://eudml.org/doc/10128
ER -

References

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