Special foliations on CP2 with a unique singular point

被引：0
|
作者：
Alcantara, Claudia R. [1 ]
机构：
[1] Univ Guanajuato, Dept Matemat, Callejon Jalisco S-N,Ap 402, Guanajuato 36000, Gto, Mexico
来源：
RESEARCH IN THE MATHEMATICAL SCIENCES | 2022年 / 9卷 / 01期
关键词：
Foliation; Algebraic leaf; Singular point; Logarithmic foliation;
D O I：
10.1007/s40687-022-00311-9
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this work, we construct, for any d >= 2, a new foliation on CP2 of degree d with a unique singular point of multiplicity d - 1 without invariant algebraic curves that contain all its separatrices. We also prove that if X is a foliation on CP2 with a unique nilpotent singular point, then X has no algebraic leaves. Finally, we characterize logarithmic foliations on CP2 with a unique singular point. And we give some new examples of this kind of foliations.
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页数：11
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