Lehmann-Suwa Residues Of Codimension One Holomorphic Foliations And Applications

• Autores: Fern´Andez-P´Erez A., T´Amara J.
• Formato: artículo
• Fecha de Publicación: 2020
• Institución: Consejo Nacional de Ciencia Tecnología e Innovación
• Repositorio: CONCYTEC-Institucional
• Lenguaje: inglés
• OAI Identifier: oai:repositorio.concytec.gob.pe:20.500.12390/2653
• Enlace del recurso: https://hdl.handle.net/20.500.12390/2653; https://doi.org/10.4310/AJM.2020.v24.n4.a6
• Nivel de acceso: acceso abierto
• Materia: Residues formula; holomorphic foliations; Levi-flat hypersurfaces; http://purl.org/pe-repo/ocde/ford#2.07.01

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. © 2020 International Press