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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Projective normality of abelian varieties

Author: Jaya N. Iyer
Journal: Trans. Amer. Math. Soc. 355 (2003), 3209-3216
MSC (2000): Primary 14C20, 14K05, 14K25, 14N05
Published electronically: April 16, 2003
MathSciNet review: 1974682
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Abstract: We show that ample line bundles $L$ on a $g$-dimensional simple abelian variety $A$, satisfying $h^0(A,L)>2^g\cdot g!$, give projective normal embeddings, for all $g\geq 1$.

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  • [1] Iyer, J.: Projective normality of abelian surfaces given by primitive line bundles, Manuscripta Math., 98, 139-153 (1999). MR 2000b:14056
  • [2] Koizumi, S.: Theta relations and projective normality of abelian varieties, American Journal of Mathematics, 98, 865-889 (1976). MR 58:702
  • [3] Lange, H. and Birkenhake, Ch. : Complex abelian varieties, Grundlehren der Mathematischen Wissenschaften, 302, Springer-Verlag, Berlin, (1992). MR 94j:14001
  • [4] Lazarsfeld, R.: Projectivité normale des surfaces abéliennes, Rédigé par O. Debarre. Prépublication No. 14, Europroj- C.I.M.P.A., Nice, (1990).
  • [5] Mukai, S.: Duality between $D(X)$ and $D(\hat{X})$ with its application to Picard sheaves, Nagoya Math. J., 81, 153-175 (1981). MR 82f:14036
  • [6] Mumford, D.: Prym varieties I, in: Contributions to Analysis (a collection of papers dedicated to Lipman Bers), Academic Press, New York, 325-350 (1974). MR 52:415
  • [7] Ohbuchi, A.: A note on the normal generation of ample line bundles on abelian varieties, Proc. Japan Acad. Ser. A Math. Sci. 64, 119-120 (1988). MR 90a:14062a
  • [8] Pareschi, G.: Syzygies of abelian varieties, J. Amer. Math. Soc. 13, 651-664 (2000). MR 2001f:14086

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Additional Information

Jaya N. Iyer
Affiliation: Max-Planck-Institut für Mathematik, Vivatsgasse 7, D-53111, Bonn, Germany

Received by editor(s): December 5, 2001
Received by editor(s) in revised form: October 20, 2002
Published electronically: April 16, 2003
Article copyright: © Copyright 2003 American Mathematical Society