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Ramification divisors for branched coverings of \({\mathbb{P}}^ n\). (English) Zbl 0692.14006
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 L. Ein [Math. Ann. 261, 483-485 (1982; Zbl 0519.14005)].
Reviewer: H.Maeda

14E22 Ramification problems in algebraic geometry
14E20 Coverings in algebraic geometry
14N05 Projective techniques in algebraic geometry
Full Text: DOI EuDML
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