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Linear systems on abelian varieties of dimension 
Author(s):
Jaya
N.
Iyer
Journal:
Proc. Amer. Math. Soc.
130
(2002),
959-962.
MSC (1991):
Primary 14C20, 14B05, 14E25
Posted:
November 9, 2001
MathSciNet review:
1873767
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Abstract:
We show that polarisations of type  on  -dimensional abelian varieties are never very ample, if  . This disproves a conjecture of Debarre, Hulek and Spandaw. We also give a criterion for non-embeddings of abelian varieties into  -dimensional linear systems.
References:
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- [1]
- Barth, W.: Transplanting cohomology classes in complex-projective space, Amer. J. of Math. 92, 951-967, (1970). MR 44:4239
- [2]
- Birkenhake, Ch., Lange, H.: Complex abelian varieties, Springer-Verlag, Berlin, (1992). MR 94j:14001
- [3]
- Debarre, O., Hulek, K., Spandaw, J.: Very ample linear systems on abelian varieties, Math. Ann. 300, 181-202, (1994). MR 95k:14065
- [4]
- Ramanan, S.: Ample Divisors on Abelian Surfaces, Proc. London Math. Soc. (3), 51, 231-245, (1985). MR 87d:14034
- [5]
- A. Van de Ven: On the embeddings of abelian varieties in projective spaces, Ann. Mat. Pura Appl. (4), 103, 127-129, (1975). MR 51:8117
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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:
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
Posted:
November 9, 2001
Communicated by:
Michael Stillman
Copyright of article:
Copyright
2001,
American Mathematical Society
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