Ramification divisors for branched coverings of \({\mathbb{P}}^ n\) (Q583300)
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scientific article; zbMATH DE number 4132321
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Ramification divisors for branched coverings of \({\mathbb{P}}^ n\) |
scientific article; zbMATH DE number 4132321 |
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Ramification divisors for branched coverings of \({\mathbb{P}}^ n\) (English)
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1990
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Let X be a log-terminal projective variety of dimension n defined over an algebraically closed field of characteristic zero and \(f: X\to {\mathbb{P}}^ n\) a branched covering. Then it is proved that the ramification divisor R of f is an ample \({\mathbb{Q}}\)-Cartier divisor unless f is an isomorphism. This result generalizes theorem 1 of a paper by \textit{L. Ein} [Math. Ann. 261, 483-485 (1982; Zbl 0519.14005)].
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log-terminal projective variety
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branched covering
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ramification divisor
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