Available in electronic format
Available in print format		 Transacrions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(e) ISSN 0002-9947(p)
Previous issue | Table of contents | Next issue
Articles in press | Recently posted articles | Most recent issue | All issues
Previous Article | Next Article
     

Projective normality of abelian varieties

Author(s): Jaya N. Iyer
Journal: Trans. Amer. Math. Soc. 355 (2003), 3209-3216.
MSC (2000): Primary 14C20, 14K05, 14K25, 14N05
Posted: April 16, 2003
Retrieve article in: PDF DVI PostScript

Abstract | References | Similar articles | Additional information

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:

[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

Similar Articles:

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 14C20, 14K05, 14K25, 14N05

Retrieve articles in all Journals with MSC (2000): 14C20, 14K05, 14K25, 14N05

Additional Information:

Jaya N. Iyer
Affiliation: Max-Planck-Institut für Mathematik, Vivatsgasse 7, D-53111, Bonn, Germany
Email: jniyer@mpim-bonn.mpg.de

DOI: 10.1090/S0002-9947-03-03303-8
PII: S 0002-9947(03)03303-8
Received by editor(s): December 5, 2001
Received by editor(s) in revised form: October 20, 2002
Posted: April 16, 2003
Copyright of article: Copyright 2003, American Mathematical Society

  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2008, American Mathematical Society
Privacy Statement 		Search the AMSPowered by Google