Title
Lehmann-Suwa Residues Of Codimension One Holomorphic Foliations And Applications
Date Issued
01 January 2020
Access level
open access
Resource Type
journal article
Author(s)
T´Amara J.
Universidade Federal de Minas Gerais
Abstract
Let F be a singular codimension one holomorphic foliation on a compact complex manifold X of dimension at least three such that its singular set has codimension at least two. In this paper, we determine Lehmann-Suwa residues of F as multiples of complex numbers by integration currents along irreducible complex subvarieties of X. We then prove a formula that determines the Baum-Bott residue of simple almost Liouvillian foliations of codimension one, in terms of Lehmann- Suwa residues, generalizing a result of Marco Brunella. As an application, we give sufficient conditions for the existence of dicritical singularities of a singular real-analytic Levi-flat hypersurface M ⊂ X tangent to F.
Start page
653
End page
670
Volume
24
Issue
4
Language
English
OCDE Knowledge area
Matemáticas puras
Subjects
Scopus EID
2-s2.0-85101770142
Source
Asian Journal of Mathematics
ISSN of the container
10936106
Sponsor(s)
Acknowledgments. The authors wish to express his gratitude to Maurício Corrêa and Miguel Rodríguez Peña for several helpful comments concerning to work. The authors also gratefully acknowledge the anonymous referee for giving many suggestions that helped to improve the presentation of the paper. The first author was partially supported by CNPq Brazil grant number 427388/2016-3 and PRONEX/FAPERJ and the second author was partially supported by Fondecyt-Perú CG 217-2014.
Sources of information:
Directorio de Producción Científica
Scopus