Geometriae Dedicata

, Volume 117, Issue 1, pp 133–135 | Cite as

A Note on the Global Generation of Primitive Line Bundles on Abelian Varieties

  • Luis Fuentes García


Let (X,L) be a generic polarized abelian variety of dimension g and type (d 1,...,d g ). We show that L is globally generated when d 1+...+d g ≥ 2g.


Abelian surfaces primitive line bundles global generation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Birkenhake, Ch. and Lange, H.: Complex Abelian Vareties, Springer-Verlag, New York, 1992.Google Scholar
  2. 2.
    Birkenhake Ch., Lange H., Ramanan S. (1993). Primitive line bundles on abelian threefolds, Manuscripta Math 81: 299–310zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Debarre O., Hulek K., Spandaw J. (1994). Very ample linear systems on abelian varieties, Math. Ann 300:181–202zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Nagaraj D.S., Ramanan S. (1995). Polarisations of type (1,2,...  ,2) on abelian varieties, Duke Math. J 80(1):157–194zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Rubei E. Projective normality of abelian varieties with a line bundle of type (2,...), Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8) 1 (2) (1998), 361–367Google Scholar

Copyright information

© Springer 2006

Authors and Affiliations

  • Luis Fuentes García
    • 1
  1. 1.ETSI de Caminos Canales y PuertosUniversidad de CoruñaCoruñaSpain

Personalised recommendations