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
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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
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Sumario: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.