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

Author(s): Jaya N. Iyer
Journal: Proc. Amer. Math. Soc. 130 (2002), 959-962.
MSC (1991): Primary 14C20, 14B05, 14E25
Posted: November 9, 2001
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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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Barth, W.: Transplanting cohomology classes in complex-projective space, Amer. J. of Math. 92, 951-967, (1970). MR 44:4239

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Birkenhake, Ch., Lange, H.: Complex abelian varieties, Springer-Verlag, Berlin, (1992). MR 94j:14001

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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

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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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