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

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 _3,4² and a complete discussion on the structure of . The research is supported by President Foundation of Peking University