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.References
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Additional Information
- Sandra Di Rocco
- Affiliation: Sandra Di Rocco, Department of Mathematics, Royal Institute of Technology (KTH), 10044 Stockholm, Sweden
- MR Author ID: 606949
- Email: dirocco@math.kth.se
- Kelly Jabbusch
- Affiliation: Kelly Jabbusch, Department of Mathematics & Statistics, University of Michigan–Dearborn, 4901 Evergreen Road, Dearborn, Michigan 48128-2406 USA
- MR Author ID: 773050
- Email: jabbusch@umich.edu
- Gregory G. Smith
- Affiliation: Gregory G. Smith, Department of Mathematics & Statistics, Queen’s University, Kingston, Ontario K7L 3N6 Canada
- MR Author ID: 622959
- Email: ggsmith@mast.queensu.ca
- Received by editor(s): February 12, 2016
- Received by editor(s) in revised form: January 25, 2017, and February 1, 2017
- Published electronically: May 30, 2018
- Additional Notes: The first author was partially supported by the Vetenskapsrådet (VR) grants NT:2010-5563 and NT:2014-4736.
The second author was partially supported by the Göran Gustafsson Stiftelse.
The third author was partially supported by NSERC - © Copyright 2018 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 370 (2018), 7715-7741
- MSC (2010): Primary 14M25; Secondary 14J60, 51M20
- DOI: https://doi.org/10.1090/tran/7201
- MathSciNet review: 3852446