Foliations on of degree d with a singular point with Milnor number

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
REVISTA MATEMATICA COMPLUTENSE | 2018年 / 31卷 / 01期
关键词
Holomorphic foliation; Nilpotent singularity; Milnor number; Grobner basis; HOLOMORPHIC FOLIATIONS;
D O I
10.1007/s13163-017-0239-0
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We study holomorphic foliations on of degree d with a singular point with Milnor number and non-zero linear part. Given a foliation, using the singular scheme of the foliation and the lexicographical monomial order, we give necessary and sufficient conditions to have this kind of singularities. We show that if the singularity is nilpotent, the Grobner basis with respect to this order gives us the normal form around the singular point. Finally, we prove that these foliations have no invariant lines and we exhibit a family of foliations with a nilpotent singularity with Milnor number , for d odd.
引用
收藏
页码:187 / 199
页数:13
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