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TORIC VECTOR BUNDLES AND PARLIAMENTS OF POLYTOPES
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
Univ Michigan, Dept Math & Stat, 4901 Evergreen Rd, Dearborn, MI 48128 USA..
Queens Univ, Dept Math & Stat, Kingston, ON K7L 3N6, Canada..
2018 (English)In: Transactions of the American Mathematical Society, ISSN 0002-9947, E-ISSN 1088-6850, Vol. 370, no 11, p. 7715-7741Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
AMER MATHEMATICAL SOC , 2018. Vol. 370, no 11, p. 7715-7741
Keywords [en]
Toric vector bundle, polytopes, positivity
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-235550DOI: 10.1090/tran/7201ISI: 000444403600006Scopus ID: 2-s2.0-85055090894OAI: oai:DiVA.org:kth-235550DiVA, id: diva2:1252549
Funder
Swedish Research Council, NT: 2010-5563 NT: 2014-4736Göran Gustafsson Foundation for promotion of scientific research at Uppala University and Royal Institute of Technology
Note

QC 20181002

Available from: 2018-10-02 Created: 2018-10-02 Last updated: 2019-03-18Bibliographically approved

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