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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Cyclic coverings and higher order embeddings of algebraic varieties


Authors: Thomas Bauer, Sandra Di Rocco and Tomasz Szemberg
Journal: Trans. Amer. Math. Soc. 353 (2001), 877-891
MSC (2000): Primary 14C20
DOI: https://doi.org/10.1090/S0002-9947-00-02606-4
Published electronically: November 14, 2000
MathSciNet review: 1707697
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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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Additional Information

Thomas Bauer
Affiliation: Mathematisches Institut, Universität Erlangen-Nürnberg, Bismarckstraße $1\frac12$, D-91054 Erlangen, Germany
Address at time of publication: Fachbereich Mathematik und Informatik, Philipps-Universität Marburg, Hans-Meerwein-Straße, D-35032 Marburg, Germany
Email: tbauer@mathematik.uni-marburg.de

Sandra Di Rocco
Affiliation: KTH, Department of Mathematics, S-100 44 Stockholm, Sweden
Address at time of publication: Department of Mathematics, Yale University, PO Box 208229, Hillhouse Ave. 70, New Haven, Connecticut 05620-8229
Email: sandra.dirocco@math.yale.edu

Tomasz Szemberg
Affiliation: Instytut Matematyki, Uniwersytet Jagielloński, Reymonta 4, PL-30-059 Kraków, Poland
Address at time of publication: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
Email: szemberg@math.lsa.umich.edu

DOI: https://doi.org/10.1090/S0002-9947-00-02606-4
Received by editor(s): February 28, 1999
Received by editor(s) in revised form: June 3, 1999
Published electronically: November 14, 2000
Additional Notes: The third author was supported by a research grant of Polish Academy of Sciences and KBN grant 2 P03A 008 16
Article copyright: © Copyright 2000 American Mathematical Society