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A note on tensor products of ample line bundles on abelian varieties

Author(s): Yoshiaki Fukuma
Journal: Proc. Amer. Math. Soc. 128 (2000), 2513-2516.
MSC (1991): Primary 14C20
Posted: April 27, 2000
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Abstract: Let $(X,L)$ be a polarized abelian variety defined over the complex number field. Then we classify $(X,L)$ with $h^{0}(L)\geq 2$such that $(k+1)L$ is not $k$-jet ample nor $k$-very ample.

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Additional Information:

Yoshiaki Fukuma
Affiliation: Department of Mathematics, Faculty of Science, Tokyo Institute of Technology, Oh-okayama, Meguro-ku, Tokyo 152-8551, Japan
Address at time of publication: Department of Mathematics, Naruto University of Education, Takashima, Naruto-cho, Naruto-shi 772-8502, Japan
Email: fukuma@math.titech.ac.jp, fukuma@naruto-u.ac.jp

DOI: 10.1090/S0002-9939-00-05879-2
PII: S 0002-9939(00)05879-2
Keywords: Polarized abelian variety, $k$-jet ample, $k$-very ample
Received by editor(s): July 29, 1997
Posted: April 27, 2000
Additional Notes: The author is a Research Fellow of the Japan Society for the Promotion of Science.
Communicated by: Ron Donagi
Copyright of article: Copyright 2000, American Mathematical Society

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