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

 

On tensor products of $k$-very ample line bundles


Authors: Yukitoshi Hinohara, Kazuyoshi Takahashi and Hiroyuki Terakawa
Journal: Proc. Amer. Math. Soc. 133 (2005), 687-692
MSC (2000): Primary 14E25, 14C20; Secondary 13E10
Published electronically: September 20, 2004
MathSciNet review: 2113916
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Abstract: In this paper, we show that the tensor product of $a$-very ample and $b$-very ample line bundles on a complete algebraic variety is $(a+b)$-very ample.


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Additional Information

Yukitoshi Hinohara
Affiliation: Department of Mathematics, School of Education, Waseda University, 1-6-1 Nishi-Waseda Shinjuku-ku, Tokyo 169-8050, Japan
Address at time of publication: 389-3, Higashi-Koiso, Oiso-Mati, Naka-Gun Kanagawa, 255-0004, Japan
Email: hinohara@waseda.jp

Kazuyoshi Takahashi
Affiliation: Department of Mathematics, School of Education, Waseda University, 1-6-1 Nishi-Waseda Shinjuku-ku, Tokyo 169-8050, Japan
Address at time of publication: School of Social Sciences, Waseda University, 1-6-1 Nishi-Waseda Shinjuku-ku, Tokyo 169-8050, Japan
Email: ktaka@asagi.waseda.jp

Hiroyuki Terakawa
Affiliation: Tsuru University, 3-8-1 Tahara Tsuru-shi, Yamanashi 402-8555, Japan
Email: terakawa@tsuru.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07648-8
PII: S 0002-9939(04)07648-8
Keywords: $k$-very ampleness, tensor product, $0$-dimensional scheme, socle
Received by editor(s): December 21, 2000
Received by editor(s) in revised form: November 9, 2003
Published electronically: September 20, 2004
Communicated by: Michael Stillman
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.