MONODROMY PROBLEM AND TANGENTIAL CENTER-FOCUS PROBLEM FOR PRODUCTS OF LINES IN GENERAL POSITION IN P2

被引：0
|
作者：
Garcia, Daniel Lopez [1 ]
机构：
[1] Univ Sao Paulo IME USP, Inst Matemat & Estat, Ruado Matao 1010, BR-05508090 Sao Paulo, SP, Brazil
来源：
MOSCOW MATHEMATICAL JOURNAL | 2024年 / 24卷 / 02期
基金：
巴西圣保罗研究基金会;
关键词：
Holomorphic foliations; center problem; monodro- my action; Abelian integral; FOLIATIONS; TOPOLOGY;
D O I：
10.17323/1609-4514-2024-24-2-181-199
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider a rational map F defined by a quotient of products of lines in general position and we study the monodromy problem and the tangential center-focus problem for the fibration associated with F. Thus, we study the submodule of the 1-homology group of a regular fiber of F generated by the orbit of the monodromy action on a vanishing cycle. Moreover, we characterize the meromorphic 1-forms omega in P-2 such that the Abelian integral integral(delta t) omega vanishes on a family of cycles delta(t) around a center singularity.
引用
收藏
页码：181 / 199
页数：19
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