Polarity with respect to a foliation and Cayley-Bacharach theorems (Q2717077)
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scientific article; zbMATH DE number 1604449
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Polarity with respect to a foliation and Cayley-Bacharach theorems |
scientific article; zbMATH DE number 1604449 |
Statements
13 June 2001
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foliation
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projective plane
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subscheme of singular points
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Cayley-Bacharach theorem
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0.9007367
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0.8959946
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0.8835269
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0.88277286
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0.88137347
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0.87699884
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0.8744613
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0.87445706
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Polarity with respect to a foliation and Cayley-Bacharach theorems (English)
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The authors prove that a foliation on \({\mathbb P}^{2}\) of degree different from one and defined over an algebraically closed field is uniquely determined by the subscheme of singular points. The authors give also characterizations of the subschemes that can be singular subschemes of some foliation. The methods involve study of polarity maps and application of the Cayley-Bacharach theorem.
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