Classification of Foliations on CP^2 of degree 3 with Degenerate Singularities

Claudia R. Alcántara and Ramón Ronzón-Lavie

Journal of Singularities
volume 14 (2016), 52-73

Received 7 April 2015. Received in revised form 9 March 2016.

DOI: 10.5427/jsing.2016.14d

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Abstract:

The aim of this work is to classify foliations on CP^2 of degree 3 with degenerate singular points. For that we construct a stratification of the space of holomorphic foliations by locally closed, irreducible, non-singular algebraic subvarieties which parametrize foliations with a special degenerate singularity. We also prove that there are only two foliations with isolated singularities with automorphism group of dimension two, the maximum possible dimension. Finally we obtain the unstable foliations with only one singular point, that is, a singular point with Milnor number 13.

Keywords:

holomorphic foliation, unstable point, degenerate singularity, stratification

2000 Mathematical Subject Classification:

37F75, 14L24

Author(s) information:

Claudia R. Alcántara	Ramón Ronzón-Lavie
Departamento de Matemáticas	Departamento de Matemáticas
Universidad de Guanajuato	Universidad de Guanajuato
Callejón Jalisco s/n, A.P. 402	Callejón Jalisco s/n, A.P. 402
C.P. 36000, Guanajuato, Gto. México	C.P. 36000, Guanajuato, Gto. México
email: claudia@cimat.mx	email: ronzon@cimat.mx