Projective normality of abelian varieties
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- by Jaya N. Iyer PDF
- Trans. Amer. Math. Soc. 355 (2003), 3209-3216 Request permission
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 $g\geq 1$.References
- Jaya N. Iyer, Projective normality of abelian surfaces given by primitive line bundles, Manuscripta Math. 98 (1999), no. 2, 139–153. MR 1667600, DOI 10.1007/s002290050131
- Shoji Koizumi, Theta relations and projective normality of Abelian varieties, Amer. J. Math. 98 (1976), no. 4, 865–889. MR 480543, DOI 10.2307/2374034
- Herbert Lange and Christina Birkenhake, Complex abelian varieties, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 302, Springer-Verlag, Berlin, 1992. MR 1217487, DOI 10.1007/978-3-662-02788-2
- Lazarsfeld, R.: Projectivité normale des surfaces abéliennes, Rédigé par O. Debarre. Prépublication No. 14, Europroj- C.I.M.P.A., Nice, (1990).
- Shigeru Mukai, Duality between $D(X)$ and $D(\hat X)$ with its application to Picard sheaves, Nagoya Math. J. 81 (1981), 153–175. MR 607081, DOI 10.1017/S002776300001922X
- David Mumford, Prym varieties. I, Contributions to analysis (a collection of papers dedicated to Lipman Bers), Academic Press, New York, 1974, pp. 325–350. MR 0379510
- Akira Ohbuchi, A note on the normal generation of ample line bundles on abelian varieties, Proc. Japan Acad. Ser. A Math. Sci. 64 (1988), no. 4, 119–120. MR 966402
- Giuseppe Pareschi, Syzygies of abelian varieties, J. Amer. Math. Soc. 13 (2000), no. 3, 651–664. MR 1758758, DOI 10.1090/S0894-0347-00-00335-0
Additional Information
- Jaya N. Iyer
- Affiliation: Max-Planck-Institut für Mathematik, Vivatsgasse 7, D-53111, Bonn, Germany
- Email: jniyer@mpim-bonn.mpg.de
- Received by editor(s): December 5, 2001
- Received by editor(s) in revised form: October 20, 2002
- Published electronically: April 16, 2003
- © Copyright 2003 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 355 (2003), 3209-3216
- MSC (2000): Primary 14C20, 14K05, 14K25, 14N05
- DOI: https://doi.org/10.1090/S0002-9947-03-03303-8
- MathSciNet review: 1974682