A note on the linear systems on the projective bundles over Abelian varieties
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Abstract:
It is well known that for an ample line bundle $L$ on an Abelian variety $A$, the linear system $|2L|$ is base point free and $3L$ is very ample; moreover, the map defined by the linear system $|2L|$ 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).References
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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
- 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
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 3209313