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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
MathSciNet review: 3043004
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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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Tohru Nakashima
Affiliation: Department of Mathematical and Physical Sciences, Faculty of Science, Japan Women’s University, Mejirodai, Bunkyoku, Tokyo 112-8681, Japan

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

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