Acta Mathematica Sinica, English Series

, Volume 24, Issue 3, pp 417–430 | Cite as

Some results on special stable vector bundles of rank 3 on algebraic curves

  • Bo Han Fang
  • Xiao Jiang TanEmail author
  • Wei Yi Zhang


The authors discuss the existence and classification of stable vector bundles of rank 3, with 3 or 4 linearly independent holomorphic sections. The sets of all such bundles are denoted by ω 3,d 2 and ω 3,d 2 , respectively. Our argument leads to sufficient and necessary conditions for the existence of both kinds of bundles. The conclusion is very interesting because of its contradiction to the conjectured dimension formula of stable bundles. Finally, we give a preliminary classification of ω 3,4 2 and a complete discussion on the structure of \( \omega _{3,\tfrac{2} {3}g + 2}^3 \).


algebraic curves stable vector bundles sheaf conjectured dimension formula 


Subject Classification 14F 


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  1. [1]
    Arbarello, E., Cornalba, M., Griffiths, P. A., Harris, J., Geometry of Algebraic Curves, Springer-Verlag, 1985Google Scholar
  2. [2]
    Griffiths, P. A., Harris, J.: On the variety of special linear systems on a general algebraic curve. Duke Math. J., 47, 233–272 (1980)zbMATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    Narasimhan, M. S., Seshadri, C. S.: Stable and unitary vector bundles over an compact Riemann surface. Ann. of Math., 82, 540–567 (1965)CrossRefMathSciNetGoogle Scholar
  4. [4]
    Tan, X. J.: Some results on the existence of rank two special stable vecotr bundles. Manusripta Math., 75(4), 365–373 (1992)zbMATHGoogle Scholar
  5. [5]
    Tan, X. J.: On classification of ω 2,2g3+2/2 (in Chinese). Advances in Mathematics, 24(5), (1995)Google Scholar
  6. [6]
    Tan, X. J.: A Model of Brill-Noether Theory for Rank Two Vector Bundles and Its Petri Map. Asian J. Math., 7(4), 539–550 (2003)zbMATHMathSciNetGoogle Scholar
  7. [7]
    Texidor, M. B.: On the Gieseker-Petrimap for vector bundles of rank 2. Manuscripta Math., 75, 375–382 (1992)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.School of Mathematical SciencesPeking UniversityBeijingP. R. China

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