Stable vector bundles on curves: numerical invariants of their extremal subbundles

Abstract

Let X be a smooth projective curve of genus g ≥ 2 and E a rank r vector bundle on X.where F is a rank t subsheaf of E}. Here we construct rank r stable vector bundles E on X such that the sequence {s t (E)} 1≤t<r has a prescribed value and the set of all subsheaves of E with maximal degree may be explicitely described.