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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
Article
  • 40 Downloads

Abstract

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 \( \omega _{3,\tfrac{2} {3}g + 2}^3 \).

Keywords

algebraic curves stable vector bundles sheaf conjectured dimension formula 

MR(2000)

Subject Classification 14F 

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

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

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