Asian Journal of Mathematics

Volume 23 (2019)

Number 3

Determination of Baum–Bott residues of higher codimensional foliations

Pages: 527 – 538



Maurício Corrêa (Departamento de Matemática, Universidade Federal de Minas Gerais, Belo Horizonte, MG, Brazil)

Fernando Lourenço (Departamento de Ciências Exatas, Universidade Federal de Lavras, MG, Brazil)


Let $\mathscr{F}$ be a singular holomorphic foliation, of codimension $k$, on a complex compact manifold such that its singular set has codimension $\geq k+1$. In this work we determinate Baum–Bott residues for $\mathscr{F}$ with respect to homogeneous symmetric polynomials of degree $k + 1$. We drop the Baum–Bott’s generic hypothesis and we show that the residues can be expressed in terms of the Grothendieck residue of an one-dimensional foliation on a $(k + 1)$-dimensional disc transversal to a $(k +1)$-codimensional component of the singular set of $\mathscr{F}$. Also, we show that Cenkl’s algorithm for non-expected dimensional singularities holds dropping the Cenkl’s regularity assumption.


Baum–Bott residues, localization, holomorphic foliations, characteristic classes

2010 Mathematics Subject Classification

32A27, 32S65, 57R30

Received 26 October 2017

Accepted 2 March 2018

Published 9 July 2019