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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.
@article{ASNSP_2002_5_1_1_93_0,
author = {Mendes, Lu{\'\i}s Gustavo and Sad, Paulo},
title = {On dicritical foliations and {Halphen} pencils},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
pages = {93--109},
publisher = {Scuola normale superiore},
volume = {Ser. 5, 1},
number = {1},
year = {2002},
mrnumber = {1994803},
zbl = {1048.37050},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ASNSP_2002_5_1_1_93_0/}
}
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 SP - 93 EP - 109 VL - 1 IS - 1 PB - Scuola normale superiore UR - http://geodesic.mathdoc.fr/item/ASNSP_2002_5_1_1_93_0/ LA - en ID - ASNSP_2002_5_1_1_93_0 ER -
%0 Journal Article %A Mendes, Luís Gustavo %A Sad, Paulo %T On dicritical foliations and Halphen pencils %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2002 %P 93-109 %V 1 %N 1 %I Scuola normale superiore %U http://geodesic.mathdoc.fr/item/ASNSP_2002_5_1_1_93_0/ %G en %F ASNSP_2002_5_1_1_93_0
Mendes, Luís Gustavo; Sad, Paulo. On dicritical foliations and Halphen pencils. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 1 (2002) no. 1, pp. 93-109. http://geodesic.mathdoc.fr/item/ASNSP_2002_5_1_1_93_0/