Differentiable Invariants of Holomorphic Foliations

Rudy Rosas

doi:10.1007/s00574-022-00297-6

Differentiable Invariants of Holomorphic Foliations

Rudy Rosas

Sección de Matemáticas

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Abstract

In this paper we study differentiable equivalences of germs of singular holomorphic foliations in dimension two. We prove that the Camacho–Sad indices are invariant by such equivalences. We also prove that the Baum–Bott index is a differentiable invariant for some classes of foliations. As a corollary we show that generic degree two holomorphic foliations of P² are differentiably rigid.

Original language	English
Pages (from-to)	1107-1130
Number of pages	24
Journal	Bulletin of the Brazilian Mathematical Society
Volume	53
Issue number	4
DOIs	https://doi.org/10.1007/s00574-022-00297-6
State	Published - Dec 2022

Keywords

Baum-Bott index
Camacho-Sad index
Holomorphic foliations
Holomorphic vector fields singularities
Invariants of holomorphic foliations

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10.1007/s00574-022-00297-6

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title = "Differentiable Invariants of Holomorphic Foliations",

abstract = "In this paper we study differentiable equivalences of germs of singular holomorphic foliations in dimension two. We prove that the Camacho–Sad indices are invariant by such equivalences. We also prove that the Baum–Bott index is a differentiable invariant for some classes of foliations. As a corollary we show that generic degree two holomorphic foliations of P2 are differentiably rigid.",

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N2 - In this paper we study differentiable equivalences of germs of singular holomorphic foliations in dimension two. We prove that the Camacho–Sad indices are invariant by such equivalences. We also prove that the Baum–Bott index is a differentiable invariant for some classes of foliations. As a corollary we show that generic degree two holomorphic foliations of P2 are differentiably rigid.

AB - In this paper we study differentiable equivalences of germs of singular holomorphic foliations in dimension two. We prove that the Camacho–Sad indices are invariant by such equivalences. We also prove that the Baum–Bott index is a differentiable invariant for some classes of foliations. As a corollary we show that generic degree two holomorphic foliations of P2 are differentiably rigid.

KW - Baum-Bott index

KW - Camacho-Sad index

KW - Holomorphic foliations

KW - Holomorphic vector fields singularities

KW - Invariants of holomorphic foliations

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M3 - Article

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SP - 1107

EP - 1130

JO - Bulletin of the Brazilian Mathematical Society

JF - Bulletin of the Brazilian Mathematical Society

IS - 4

ER -

Differentiable Invariants of Holomorphic Foliations

Abstract

Keywords

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