Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

Request Permissions   Purchase Content 


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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 $.

References [Enhancements On Off] (What's this?)

  • 1. M.R. Douglas, R. Reinbacher and S.-T. Yau, Branes, bundles and attractors: Bogomolov and beyond, arXiv:math/0604597
  • 2. M. Gulbrandsen, Vector bundles and monads on abelian threefolds, arXiv:math/09073597
  • 3. H. Lange and Ch. Birkenhake, Complex abelian varieties, Springer-Verlag, 2004. MR 2062673 (2005c:14001)
  • 4. M. Maruyama, Moduli of stable sheaves II, J. Math. Kyoto Univ. 18 (1978), 557-614. MR 509499 (82h:14011)
  • 5. S. Mukai, Duality between $ D(X)$ and $ D(\widehat X)$ with its applications to Picard sheaves, Nagoya Math.J. 81 (1981), 153-175. MR 607081 (82f:14036)
  • 6. T. Nakashima, Reflection of sheaves on a Calabi-Yau variety, Asian J. Math. 6 (2002), 567-577. MR 1946347 (2004g:14043)
  • 7. T. Nakashima, Strong Bogomolov inequality for stable vector bundles, J. Geom. Phys. 57 (2007), 1977-1983. MR 2348273 (2008g:14072)
  • 8. T. Nakashima, Existence of stable bundles on Calabi-Yau manifolds, RIMS Kôkyûroku Bessatsu 9 (2008), 153-161 MR 2509698 (2010i:14075)
  • 9. R. Paoletti, Stability of a class of homogeneous vector bundles on $ \mathbb{P}^n$, Boll. Un. Mat. Ital. 9 (1995), 329-343. MR 1336240 (96f:14053)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 14J60, 14K12

Retrieve articles in all journals with MSC (2010): 14J60, 14K12

Additional Information

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

American Mathematical Society