Smooth curves possessing many linear systems \(g^ 1_ n\) (Q687384)
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scientific article; zbMATH DE number 431058
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Smooth curves possessing many linear systems \(g^ 1_ n\) |
scientific article; zbMATH DE number 431058 |
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Smooth curves possessing many linear systems \(g^ 1_ n\) (English)
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10 January 1994
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Consider smooth curves containing at least \(s\) base point free linear systems \(g^ r_ n\) (simple if \(r>0\); mutually independent if \(r=1)\). Castelnuovo gave upper bounds for the genus \(g\) of \(C\) in case \(s=1\). Accola gave upper bounds for the genus \(g\) of \(C\) in case \(s>1\) and showed that this bound is sharp. In this paper we classify curves satisfying this genus bound in case \(r=1\). In the meantime, curves having this genus bound in case \(r>5\) are also classified by L. Donohoe in his Ph.-D. Thesis.
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smooth curves containing linear systems
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