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

 

Linear systems on abelian varieties of dimension $2g+1$


Author: Jaya N. Iyer
Journal: Proc. Amer. Math. Soc. 130 (2002), 959-962
MSC (1991): Primary 14C20, 14B05, 14E25
Published electronically: November 9, 2001
MathSciNet review: 1873767
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Abstract: We show that polarisations of type $(1,...,1,2g+2)$ on $g$-dimensional abelian varieties are never very ample, if $g\geq 3$. This disproves a conjecture of Debarre, Hulek and Spandaw. We also give a criterion for non-embeddings of abelian varieties into $2g+1$-dimensional linear systems.


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Additional Information

Jaya N. Iyer
Affiliation: Institut de Mathématiques, Case 247, Université Paris-6, 4, Place Jussieu, 75252, Paris Cedex 05, France
Address at time of publication: FB6, Mathematik, Universität GH Essen, 45117 Essen, Germany
Email: iyer@math.jussieu.fr, jaya.iyer@uni-essen.de

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06264-5
PII: S 0002-9939(01)06264-5
Received by editor(s): May 10, 2000
Received by editor(s) in revised form: October 10, 2000
Published electronically: November 9, 2001
Communicated by: Michael Stillman
Article copyright: © Copyright 2001 American Mathematical Society