Codimension one foliations of degree three on projective spaces

被引：4

作者：

da Costa, Raphael Constant ^{[1
]}

Lizarbe, Ruben ^{[1
]}

Pereira, Jorge Vitorio ^{[2
]}

机构：

[1] Univ Estado Rio de Janeiro, UERJ, Rua Sao Francisco Xavie 524, BR-20550900 Maracana, RJ, Brazil

[2] IMPA, Estr Dona Castorina 110, BR-22460320 Rio De Janeiro, Brazil

来源：

BULLETIN DES SCIENCES MATHEMATIQUES | 2022年 / 174卷

关键词：

Foliations on projective spaces; Spaces of foliations; Degree three foliations; IRREDUCIBLE COMPONENTS; HOLOMORPHIC FOLIATIONS; STABILITY; SINGULARITIES;

D O I：

10.1016/j.bulsci.2021.103092

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We establish a structure theorem for degree three codimension one foliations on projective spaces of dimension n >= 3, extending a result by Loray, Pereira, and Touzet for degree three foliations on P-3. We show that the space of codimension one foliations of degree three on P-n, n >= 3, has exactly 18 distinct irreducible components parameterizing foliations without rational first integrals, and at least 6 distinct irreducible components parameterizing foliations with rational first integrals. (C) 2021 Elsevier Masson SAS. All rights reserved.

引用

页数：39

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