Please use this identifier to cite or link to this item: http://repositorio.ufla.br/jspui/handle/1/59499
Title: A brief survey on residue theory of holomorphic foliations
Keywords: Holomorphic foliation
Flags
Residues
Characteristic classes
Issue Date: 2023
Publisher: Sociedade Brasileira de Matemática
Citation: LOURENÇO, F.; REIS, F. A brief survey on residue theory of holomorphic foliations. Revista Matemática Contemporânea. [S.l], v. 53, p.181-2012, 2023.
Abstract: This is a survey paper dealing with holomorphic foliations, with emphasis on Residue Theory and its applications. We start recalling the definition of holomorphic foliations as a subsheaf of the tangent sheaf of a manifold. The theory of Characteristic Classes of vector bundles is approached from this perspective. We define Chern Class of holomorphic foliations using the Chern-Weil theory and we remark that the Baum-Bott residue is a great tool that help us to classify some foliations. We present along the survey several recent results and advances in residue theory. We finish the work present some applications of residues to solve for example the Poincaré problem and the existence of minimal sets for foliations.
URI: https://mc.sbm.org.br/wp-content/uploads/sites/9/sites/9/2023/08/Article-08-vol-53.pdf
http://repositorio.ufla.br/jspui/handle/1/59499
Appears in Collections:DMM - Artigos publicados em periódicos

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