Foliations on P^2 admitting a primitive model

Gilberto D. Cuzzuol and Rogério S. Mol

Journal of Singularities
volume 3 (2011), 8-19

Received: 2 September 2010. Received in revised form: 11 February 2011.

DOI: 10.5427/jsing.2011.3b

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Abstract:

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^~.

Keywords:

Holomorphic foliation, polar varieties, linear systems

Mathematical Subject Classification:

Primary 32S65 ; Secondary 14C21

Author(s) information:

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: gilcuzzuol@unifei.edu.br	email: rsmol@mat.ufmg.br