On dicritical foliations and Halphen pencils
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 1 (2002) no. 1, p. 93-109

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},
     publisher = {Scuola normale superiore},
     volume = {Ser. 5, 1},
     number = {1},
     year = {2002},
     pages = {93-109},
     zbl = {1048.37050},
     mrnumber = {1994803},
     language = {en},
     url = {http://www.numdam.org/item/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, Serie 5, Volume 1 (2002) no. 1, pp. 93-109. http://www.numdam.org/item/ASNSP_2002_5_1_1_93_0/

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