Second type foliations of codimension one

被引：0

作者：

Cuzzuol, Gilberto ^{[1
]}

Mol, Rogerio ^{[2
]}

机构：

[1] Univ Fed Itajuba, Dept Matemat, Rua Irma Ivone Drumond 200, BR-35903087 Itabira, MG, Brazil

[2] Univ Fed Minas Gerais, Dept Matemat, Av Antonio Carlos 6627, BR-30123970 Belo Horizonte, MG, Brazil

来源：

BOLETIN DE LA SOCIEDAD MATEMATICA MEXICANA | 2019年 / 25卷 / 03期

关键词：

Holomorphic foliations; Invariant varieties; Equidesingularization; SINGULAR HOLOMORPHIC FOLIATIONS; REDUCTION; EXISTENCE;

D O I：

10.1007/s40590-018-0207-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article, for holomorphic foliations of codimension one at (C-3, 0), we define the family of second type foliations. This is formed by foliations having, in the reduction process by blow-up maps, only well-oriented singularities, meaning that the reduction divisor does not contain weak separatrices of saddle-node singularities. We prove that the reduction of singularities of a non-dicritical foliation of the second type coincides with the desingularization of its set of separatrices.

引用

页码：619 / 635

页数：17

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