On dicritical foliations and Halphen pencils

Luís Gustavo Mendes; Paulo Sad

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2002)

  • Volume: 1, Issue: 1, page 93-109
  • ISSN: 0391-173X

Abstract

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The aim of this article is to provide information on the number and on the geometrical position of singularities of holomorphic foliations of the projective plane. As an application it is shown that certain foliations are in fact Halphen pencils of elliptic curves. The results follow from Miyaoka’s semipositivity theorem, combined with recent developments on the birational geometry of foliations.

How to cite

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Mendes, Luís Gustavo, and Sad, Paulo. "On dicritical foliations and Halphen pencils." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 1.1 (2002): 93-109. <http://eudml.org/doc/84469>.

@article{Mendes2002,
abstract = {The aim of this article is to provide information on the number and on the geometrical position of singularities of holomorphic foliations of the projective plane. As an application it is shown that certain foliations are in fact Halphen pencils of elliptic curves. The results follow from Miyaoka’s semipositivity theorem, combined with recent developments on the birational geometry of foliations.},
author = {Mendes, Luís Gustavo, Sad, Paulo},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {holomorphic foliation; singularity; complex projective plane},
language = {eng},
number = {1},
pages = {93-109},
publisher = {Scuola normale superiore},
title = {On dicritical foliations and Halphen pencils},
url = {http://eudml.org/doc/84469},
volume = {1},
year = {2002},
}

TY - JOUR
AU - Mendes, Luís Gustavo
AU - Sad, Paulo
TI - On dicritical foliations and Halphen pencils
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2002
PB - Scuola normale superiore
VL - 1
IS - 1
SP - 93
EP - 109
AB - The aim of this article is to provide information on the number and on the geometrical position of singularities of holomorphic foliations of the projective plane. As an application it is shown that certain foliations are in fact Halphen pencils of elliptic curves. The results follow from Miyaoka’s semipositivity theorem, combined with recent developments on the birational geometry of foliations.
LA - eng
KW - holomorphic foliation; singularity; complex projective plane
UR - http://eudml.org/doc/84469
ER -

References

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  16. [Po] H. Poincaré, Sur l’intégration algébrique des équations différentielles du 1er ordre et du 1er degré, Rend. Circ. Mat. Palermo 5 (1891), 161-191. JFM23.0319.01
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