Numerically effective line bundles associated to a stable bundle over a curve

Abstract

Let G be a complex semisimple group and χ a character of a parabolic subgroup Psubset ofG such that the associated line bundle on G/P is ample. For a general stable G-bundle E_G over a compact Riemann surface of genus at least two, the line bundle Image over E_G/P defined by χ has the property that the restriction of Image to any closed subvariety of E_G/P of smaller dimension is ample, although Image is not ample.