The variety of plane curves with ordinary singularities is not irreducible (Q2729310)
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scientific article; zbMATH DE number 1622405
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The variety of plane curves with ordinary singularities is not irreducible |
scientific article; zbMATH DE number 1622405 |
Statements
22 July 2001
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plane curve
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equisingularity
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\(m\)-fold singularity
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fundamental group
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The variety of plane curves with ordinary singularities is not irreducible (English)
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This paper is concerned with the existence of families of projective plane curves with given singularities. The main result is: NEWLINENEWLINENEWLINETheorem. Let \(m\geq 9\). There exists an equisingular family (ESF) of irreducible plane curves with \(r\) ordinary \(m\)-fold points as only singularities having at least one smooth component of the expected dimension and at least one component of a nonexpected dimension. Moreover the fundamental group \(\pi_{1}(\mathbb P^2\setminus C)\) is abelian for any curve \(C\) in the ESF.
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