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A note on the linear systems on the projective bundles over Abelian varieties


Author: Lei Zhang
Journal: Proc. Amer. Math. Soc. 142 (2014), 2569-2580
MSC (2010): Primary 14E05; Secondary 14K99
DOI: https://doi.org/10.1090/S0002-9939-2014-11982-4
Published electronically: April 10, 2014
MathSciNet review: 3209313
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Abstract: It is well known that for an ample line bundle $ L$ on an Abelian variety $ A$, the linear system $ \vert 2L\vert$ is base point free and $ 3L$ is very ample; moreover, the map defined by the linear system $ \vert 2L\vert$ is well understood (cf. Theorem 1.1). In this paper we generalize this classical result and give a new proof using the theory developed by Pareschi and Popa in 2011 (cf. Theorem 1.2).


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Additional Information

Lei Zhang
Affiliation: College of Mathematics and Information Sciences, Shaanxi Normal University, Xi’an 710062, People’s Republic of China
Email: lzhpkutju@gmail.com

DOI: https://doi.org/10.1090/S0002-9939-2014-11982-4
Keywords: Abelian varieties, linear system, birational maps
Received by editor(s): March 18, 2012
Received by editor(s) in revised form: July 27, 2012
Published electronically: April 10, 2014
Communicated by: Lev Borisov
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.