Differentiable Invariants of Holomorphic Foliations

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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 languageEnglish
Pages (from-to)1107-1130
Number of pages24
JournalBulletin of the Brazilian Mathematical Society
Issue number4
StatePublished - Dec 2022


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


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