Cyclic coverings and higher order embeddings of algebraic varieties

Bauer, Thomas; Di Rocco, Sandra; Szemberg, Tomasz

doi:10.1090/S0002-9947-00-02606-4

Cyclic coverings and higher order embeddings of algebraic varieties
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by Thomas Bauer, Sandra Di Rocco and Tomasz Szemberg

Trans. Amer. Math. Soc. 353 (2001), 877-891

DOI: https://doi.org/10.1090/S0002-9947-00-02606-4

Published electronically: November 14, 2000

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Abstract:

In the present paper we study higher order embeddings in the context of cyclic coverings. Analyzing the positivity of the line bundle downstairs and its relationship with the branch divisor, we provide criteria for its pull-back to define an embedding of given order. We show that the obtained criteria are sharp. Finally, we apply them to various – sometimes seemingly unrelated–problems in algebraic geometry.

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