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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Large families of stable bundles on abelian varieties


Author: Tohru Nakashima
Journal: Proc. Amer. Math. Soc. 141 (2013), 2225-2231
MSC (2010): Primary 14J60; Secondary 14K12
Published electronically: February 20, 2013
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Abstract: A sequence of $ \mu $-stable bundles $ \{E_m\}$ on a polarized variety $ (X,H)$ is said to be a large family if their ranks and the discriminants become arbitrarily large as $ m$ goes to infinity. We prove the existence of large families on a principally polarized abelian variety $ (X,\Theta )$ such that the Neron-Severi group is generated by $ \Theta $.


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Additional Information

Tohru Nakashima
Affiliation: Department of Mathematical and Physical Sciences, Faculty of Science, Japan Women’s University, Mejirodai, Bunkyoku, Tokyo 112-8681, Japan
Email: nakashima@fc.jwu.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11559-5
PII: S 0002-9939(2013)11559-5
Keywords: Stable vector bundles, abelian varieties
Received by editor(s): May 11, 2011
Received by editor(s) in revised form: October 9, 2011
Published electronically: February 20, 2013
Additional Notes: The author was supported in part by Grant-in-Aid for Scientific Research (C)(21540049)
The author is grateful to the referee for pointing out several mistakes in the original manuscript and for giving valuable comments
Communicated by: Lev Borisov
Article copyright: © Copyright 2013 American Mathematical Society