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Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations
- Publisher
- Springer Journals
- Copyright
- Copyright © Sociedade Brasileira de Matemática 2022
- ISSN
- 1678-7544
- eISSN
- 1678-7714
- DOI
- 10.1007/s00574-022-00297-6
- Publisher site
- See Article on Publisher Site
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\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$${\mathbb {P}}^2$$\end{document} are differentiably rigid.
Journal
"Bulletin of the Brazilian Mathematical Society, New Series" – Springer Journals
Published: Dec 1, 2022
Keywords: Holomorphic foliations; Holomorphic vector fields singularities; Camacho-Sad index; Baum-Bott index; Invariants of holomorphic foliations