Toric vector bundles and parliaments of polytopes

Di Rocco, Sandra; Jabbusch, Kelly; Smith, Gregory

doi:10.1090/tran/7201

Toric vector bundles and parliaments of polytopes
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by Sandra Di Rocco, Kelly Jabbusch and Gregory G. Smith PDF

Trans. Amer. Math. Soc. 370 (2018), 7715-7741 Request permission

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 relate edges to jets. Using the polytopes, we also exhibit vector bundles that are ample but not globally generated, and vector bundles that are ample and globally generated but not very ample.

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