Complex foliations with algebraic limit sets

被引:0
作者
Camacho, C [1 ]
Scárdua, BA [1 ]
机构
[1] IMPA, BR-22460320 Rio De Janeiro, Brazil
关键词
holomorphic foliation; limit set; holonomy;
D O I
暂无
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We regard the problem of classification for complex projective foliations with algebraic limit sets and prove the following: Let F be a holomorphic foliation by curves in the complex projective plane CP(2) having as limit set some singularities and an algebraic curve Lambda subset of CP(2). If the singularities sing F boolean AND Lambda are generic then either F is given by a closed rational 1-form or it is a rational pull-back gi a Riccati foliation R : p(x)dy - (a(x)y(2) + b(x)y)dx = 0, where Lambda corresponds to <(y = 0)over bar> boolean OR <(p(x) = 0)over bar>, on (C) over bar x (C) over bar. The proof is based on the solvability of the generalized holonomy groups associated to a reduction process of the singularities sing F boolean AND Lambda and the construction of an affine transverse structure for F outside an algebraic curve containing Lambda.
引用
收藏
页码:57 / 88
页数:32
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