Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Toric vector bundles and parliaments of polytopes


Authors: Sandra Di Rocco, Kelly Jabbusch and Gregory G. Smith
Journal: Trans. Amer. Math. Soc.
MSC (2010): Primary 14M25; Secondary 14J60, 51M20
DOI: https://doi.org/10.1090/tran/7201
Published electronically: May 30, 2018
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 14M25, 14J60, 51M20

Retrieve articles in all journals with MSC (2010): 14M25, 14J60, 51M20


Additional Information

Sandra Di Rocco
Affiliation: Sandra Di Rocco, Department of Mathematics, Royal Institute of Technology (KTH), 10044 Stockholm, Sweden
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
Email: jabbusch@umich.edu

Gregory G. Smith
Affiliation: Gregory G. Smith, Department of Mathematics & Statistics, Queen’s University, Kingston, Ontario K7L 3N6 Canada
Email: ggsmith@mast.queensu.ca

DOI: https://doi.org/10.1090/tran/7201
Keywords: Toric vector bundle, polytopes, positivity
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\nobreakdash-5563 and NT:2014\nobreakdash-4736.
The second author was partially supported by the Göran Gustafsson Stiftelse.
The third author was partially supported by NSERC
Article copyright: © Copyright 2018 American Mathematical Society

American Mathematical Society