A generalization of the existence theorem of special line bundles

Abstract

LetX be a generic smooth irreducible complex projective curve of genusg withg≥4. In this paper, we generalize the existence theorem of special divisors to high dimensional indecomposable vector bundles. We give a necessary and sufficient condition on the existence ofn-dimensional indecomposable vector bundlesE onX with det(E)=d, dimH0(X,E)≥h. We also determine under what condition the set of all such vector bundles will be finite and how many elements it contains.