Toric vector bundles and parliaments of polytopes

2014/09/30 by Sandra Di Rocco, Kelly Jabbusch, Gregory G. Smith · 1 citation
Mathematics · #math.AG #msc:14M25

paper · pdf · doi:10.1090/tran/7201

published as Transactions of the American Mathematical Society 370 (2018) 7715-7741 · 24 pages, 5 figures

arxiv created 2017/02/01 · arxiv updated 2019/02/08

Abstract

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

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