Journal of Singularities
volume 3 (2011), 8-19
Received: 2 September 2010. Received in revised form: 11 February 2011.
Given a foliation F on P^2, by fixing a line L&sub P^2 , the polar pencil of F with axis L is the set of all polar curves of F with respect to points l in L. In this work we study foliations F which admit a polar pencil whose generic element is reducible. To such an F is associated a primitive model, which is a foliation F~ whose polar pencil, besides having irreducible generic element, is such that its fibers are contained in those of the polar pencil of F. This work focuses on relating geometric properties of a foliation F with those of its primitive model F~.
Mathematical Subject Classification:
Primary 32S65 ; Secondary 14C21
|Gilberto D. Cuzzuol||Rogério S. Mol|
|Departamento de Matemática||Departamento de Matemática|
|Universidade Federal de Itajubá||Universidade Federal de Minas Gerais|
|Rua São Paulo, 377||Av. Antônio Carlos, 6627, C.P. 702|
|35900-373 - Itabira - MG, Brazil||30123-970 - Belo Horizonte - MG, Brazil|
|email: email@example.com||email: firstname.lastname@example.org|