Number of singularities of a foliation on \({\mathbb P}^n\) (Q2750888)
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scientific article; zbMATH DE number 1663133
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Number of singularities of a foliation on \({\mathbb P}^n\) |
scientific article; zbMATH DE number 1663133 |
Statements
21 October 2001
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singularities
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foliations
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multiplicity
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Chern class
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Baum-Bott formula
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degree
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0.91631436
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0.9138332
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0.90726537
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0.8868744
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0.88131225
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Number of singularities of a foliation on \({\mathbb P}^n\) (English)
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The author proves a generalization of the classical Baum-Bott formula for the number of singularities of a \(1\)-dimensional foliation on a projective space. NEWLINENEWLINENEWLINELet \(m\) be the dimension of the singular locus of a foliation. He gives an upper bound for the number of singularities of dimension \(m\), counted with multiplicity and degree, in terms of the degree of the foliation. NEWLINENEWLINENEWLINEIn the last section a general formula for \(r\)-dimensional foliation on a smooth projective variety is presented.
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