Toric vector bundles and parliaments of polytopes

Sandra Di Rocco, Kelly Jabbusch, Gregory G. Smith

Published 2014-09-10Version 1

We introduce a collection of rational convex polytopes associated to a toric vector bundle on a smooth complete toric variety. We show that the lattice points in the polytopes correspond to generators for the space of global sections and we relate edges to jets. Using the polytopes, we also exhibit bundles that are ample but not globally generated, and bundles that are ample and globally generated but not very ample.