Non-globally Generated Bundles on Curves

Abstract

Abstract We describe the locus of stable bundles on a smooth genus $g$ curve that fail to be globally generated. For each rank $r$ and degree $d$ with $rg<d<r(2g-1)$, we exhibit a component of the expected dimension. We show, moreover, that no component has larger dimension and give an explicit description of those families of smaller dimension than expected. For large-enough degrees, we show that the locus is irreducible.