Singularities of logarithmic foliations

A logarithmic 1-form on ℂℙn can be written as ω = (Π0m Fj) ∑0m λi dFi/Fi = λ0F̂ 0dF0 +⋯+ λmF̂ mdFm with F̂i = (Π0 m Fj)/Fi for some homogeneous polynomials Fi of degree di and constants λi ∈ ℂ* such that ∑ λidi = 0. For general Fi, λi, the singularities of ω consist of a schematic union of the codim...

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Detalles Bibliográficos
Autor principal: Cukierman, Fernando
Publicado: 2006
Materias:
Characteristic classes
Excess intersection
Holomorphic foliations
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0010437X_v142_n1_p131_Cukierman
http://hdl.handle.net/20.500.12110/paper_0010437X_v142_n1_p131_Cukierman
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_0010437X_v142_n1_p131_Cukierman
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spelling paper:paper_0010437X_v142_n1_p131_Cukierman2023-06-08T14:34:20Z Singularities of logarithmic foliations Cukierman, Fernando Characteristic classes Excess intersection Holomorphic foliations A logarithmic 1-form on ℂℙn can be written as ω = (Π0m Fj) ∑0m λi dFi/Fi = λ0F̂ 0dF0 +⋯+ λmF̂ mdFm with F̂i = (Π0 m Fj)/Fi for some homogeneous polynomials Fi of degree di and constants λi ∈ ℂ* such that ∑ λidi = 0. For general Fi, λi, the singularities of ω consist of a schematic union of the codimension 2 subvarieties Fi = Fj = 0 together with, possibly, finitely many isolated points. This is the case when all Fi are smooth and in general position. In this situation, we give a formula which prescribes the number of isolated singularities. © Foundation Compositio Mathematica 2006. Fil:Cukierman, F. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2006 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0010437X_v142_n1_p131_Cukierman http://hdl.handle.net/20.500.12110/paper_0010437X_v142_n1_p131_Cukierman
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Characteristic classes
Excess intersection
Holomorphic foliations
spellingShingle Characteristic classes
Excess intersection
Holomorphic foliations
Cukierman, Fernando
Singularities of logarithmic foliations
topic_facet Characteristic classes
Excess intersection
Holomorphic foliations
description A logarithmic 1-form on ℂℙn can be written as ω = (Π0m Fj) ∑0m λi dFi/Fi = λ0F̂ 0dF0 +⋯+ λmF̂ mdFm with F̂i = (Π0 m Fj)/Fi for some homogeneous polynomials Fi of degree di and constants λi ∈ ℂ* such that ∑ λidi = 0. For general Fi, λi, the singularities of ω consist of a schematic union of the codimension 2 subvarieties Fi = Fj = 0 together with, possibly, finitely many isolated points. This is the case when all Fi are smooth and in general position. In this situation, we give a formula which prescribes the number of isolated singularities. © Foundation Compositio Mathematica 2006.
author Cukierman, Fernando
author_facet Cukierman, Fernando
author_sort Cukierman, Fernando
title Singularities of logarithmic foliations
title_short Singularities of logarithmic foliations
title_full Singularities of logarithmic foliations
title_fullStr Singularities of logarithmic foliations
title_full_unstemmed Singularities of logarithmic foliations
title_sort singularities of logarithmic foliations
publishDate 2006
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0010437X_v142_n1_p131_Cukierman
http://hdl.handle.net/20.500.12110/paper_0010437X_v142_n1_p131_Cukierman
work_keys_str_mv AT cukiermanfernando singularitiesoflogarithmicfoliations
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