Nef cone of flag bundles over a curve

Abstract

Let X be a smooth projective curve defined over an algebraically closed field k, and let E be a vector bundle on X. Let OGrr(E) (1) be the tautological line bundle over the Grassmann bundle Grr (E) parameterizing all the r-dimensional quotients of the fibers of E. We give necessary and sufficient conditions for OGrr(E) (1) to be ample and nef, respectively. As an application, we compute the nef cone of Grr (E). This yields a description of the nef cone of any flag bundle over X associated to E. © 2014 by Kyoto University.