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arXiv · 1409.3109

Toric vector bundles and parliaments of polytopes

Sandra Di Rocco·Kelly Jabbusch·Gregory G. Smith
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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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Sandra Di Rocco, Kelly Jabbusch, Gregory G. Smith. 2017-02-01. Toric vector bundles and parliaments of polytopes. https://doi.org/10.1090/tran%2F7201

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