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

Author(s): Yukitoshi Hinohara; Kazuyoshi Takahashi; Hiroyuki Terakawa
Journal: Proc. Amer. Math. Soc. 133 (2005), 687-692.
MSC (2000): Primary 14E25, 14C20; Secondary 13E10
Posted: September 20, 2004
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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.

References:

1.
E. Ballico and M. C. Beltrametti, On $2$-spannedness for the adjunction mapping, Manuscripta Math. 61 (1988), 447-458. MR 0952089 (89i:14003)

2.
M. C. Beltrametti, P. Francia and A. J. Sommese, On Reider's method and higher order embeddings, Duke Math. J. 58 (1989), 425-439. MR 1016428 (90h:14021)

3.
M. C. Beltrametti and A. J. Sommese, On $k$-spannedness for projective surfaces, Algebraic Geometry, Proc. L'Aquila 1988, Lecture Notes in Math. 1417, Springer-Verlag, 1990, pp.24-51. MR 1040549 (91g:14029)

4.
M. C. Beltrametti and A. J. Sommese, (with an appendix by L. Göttsche), Zero cycles and $k$-th order embeddings of smooth projective surfaces, Proc. Projective Surfaces and their Classification, Cortona 1988, Sympos. Math. 32, INDAM, Academic Press, 1992, pp.33-48. MR 1273371 (95d:14005)

5.
M. C. Beltrametti and A. J. Sommese, On $k$-jet ampleness, Complex Analysis and Geometry, Plenum Press, 1993, pp.355-376. MR 1211891 (94g:14006)

6.
M. C. Beltrametti and A. J. Sommese, On the preservation of $k$-very ampleness under adjunction, Math. Z. 212 (1993), 257-283. MR 1202811 (94a:14002)

7.
W. Bruns and J. Herzog, Cohen-Macaulay Rings, Cambridge Stud. Adv. Math. 39, Cambridge Univ. Press, 1993. MR 1251956 (95h:13020)

8.
I. Kaplansky, Commutative Rings, Revised Edition, The Univ. of Chicago Press, 1974. MR 0345945 (49:10674)

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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: 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
Posted: September 20, 2004
Communicated by: Michael Stillman
Copyright of article: Copyright 2004, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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