ON CLIFFORD'S THEOREM FOR VECTOR BUNDLES ON ALGEBRAIC CURVES

Abstract

Let X be a smooth projective curve of genus g ≥ 2 and E a rank r spanned vector bundle on X with deg(E)/rank(E) ≤ g − 1. Here we give lower bounds for deg(E) refining the classical theorem of Clifford. Most results are for vector bundles with rank ≤ 5.