On the singularities of simple plane curves (Q1061369)
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scientific article; zbMATH DE number 3911235
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the singularities of simple plane curves |
scientific article; zbMATH DE number 3911235 |
Statements
On the singularities of simple plane curves (English)
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1985
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Consider a simple closed curve in the projective plane which is (directly) differentiable, has even order, and meets every line. The only possible singularities are inflections, cusps, and beaks. Let their numbers be \(n_ 1\), \(n_ 2\), \(n_ 3\) respectively. It is shown that \(n_ 1+n_ 2+n_ 3\geq 3\), and if \(n_ 2>0\), then \(n_ 1+2n_ 2+n_ 3\geq 6\).
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singularities
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inflections
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cusps
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beaks
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