Splitting of vector bundles on algebraic curves and elementary transformations

Abstract

Let Ebe a rank nvector bundle on a smooth projective curve X. It is known that Emay be obtained from a splitted bundle +1≤i≤ L_i;, rank(L_i) = 1, by a finite number of elementary transformations. Here we give upper bounds for their minimal number. If n= 2 this is related to the order of stability of E.