A Generalization of the Existence Theorem of Special Line Bundles

Let X be a generic smooth irreducibile complex projective curve of genus g with a g . 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 exestence of n-dimensional indecomposable vector bundles E on X with det(E)= d, dim H. (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.