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
相关论文
共 50 条
  • [31] On the local structure of ω-limit sets of maps
    Brunovsky, P
    Polacik, P
    ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 1997, 48 (06): : 976 - 986
  • [32] Limit sets for complete minimal immersions
    Antonio Alarcón
    Nikolai Nadirashvili
    Mathematische Zeitschrift, 2008, 258 : 107 - 113
  • [33] LIMIT SETS IN IMPULSIVE SEMIDYNAMICAL SYSTEMS
    Ding, Changming
    TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, 2014, 43 (01) : 97 - 115
  • [34] Foliations on CP2 with a unique singular point without invariant algebraic curves
    Alcantara, Claudia R.
    Pantaleon-Mondragon, Rubi
    GEOMETRIAE DEDICATA, 2020, 207 (01) : 193 - 200
  • [35] Invariant sets and nilpotency of endomorphisms of algebraic sofic shifts
    Ceccherini-Silberstein, Tullio
    Coornaert, Michel
    Phung, Xuan Kien
    ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2024, 44 (10) : 2859 - 2900
  • [36] ON THE LIMIT SETS OF SPHERICAL C R MANIFOLDS
    Kamishima, Yoshinobu
    Odebiyi, Omolola
    BULLETIN OF THE INSTITUTE OF MATHEMATICS ACADEMIA SINICA NEW SERIES, 2009, 4 (02): : 189 - 217
  • [37] On Limit Sets of Monotone Maps on Regular Curves
    Aymen Daghar
    Habib Marzougui
    Qualitative Theory of Dynamical Systems, 2021, 20
  • [38] Projective BGG equations, algebraic sets, and compactifications of Einstein geometries
    Cap, A.
    Gover, A. R.
    Hammerl, M.
    JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2012, 86 : 433 - 454
  • [39] Remarks on limit sets of infinite iterated function systems
    Hille, Martial R.
    MONATSHEFTE FUR MATHEMATIK, 2012, 168 (02): : 215 - 237
  • [40] Limit Sets of Cellular Automata Associated to Probability Measures
    Petr Kůrka
    Alejandro Maass
    Journal of Statistical Physics, 2000, 100 : 1031 - 1047