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On strengthening of the Kleiman-Chevalley projectivity criterion


Author: Michał Farnik
Journal: Proc. Amer. Math. Soc. 141 (2013), 4005-4013
MSC (2010): Primary 51N35; Secondary 14A10, 14M25
DOI: https://doi.org/10.1090/S0002-9939-2013-11695-3
Published electronically: July 10, 2013
MathSciNet review: 3091791
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Abstract: We discuss the possibilities of strengthening the classical Kleiman-Chevalley projectivity criterion by exploring the properties of the Picard number and the maximal quasiprojective open subsets of a variety. We also prove two theorems which give a bound on how much the criterion can be strengthened.


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Additional Information

Michał Farnik
Affiliation: Instytut Matematyczny, Polska Akademia Nauk, św. Tomasza 30, 31-027 Kraków, Poland
Address at time of publication: Instytut Matematyczny, Polska Akademia Nauk, Śniadeckich 8, 00-956 Warszawa, Poland
Email: michal.farnik@gmail.com

DOI: https://doi.org/10.1090/S0002-9939-2013-11695-3
Keywords: Picard number, maximal open quasiprojective set, Chevalley projectivity criterion, nonprojective varieties, toric varieties.
Received by editor(s): June 15, 2011
Received by editor(s) in revised form: January 7, 2012
Published electronically: July 10, 2013
Additional Notes: The author was partially supported by Polish MNiSW grant N N201 611740, 2011–2012
Communicated by: Lev Borisov
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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