Okounkov bodies on projectivizations of rank two toric vector bundles

Details Okounkov bodies on projectivizations of rank two toric vector bundles Okounkov bodies on projectivizations of rank two toric vector bundles

2009-11-12

arxiv.org/abs/0911.2287v2

Mathematics

Algebraic Geometry

26 pages, 2 figures; v.2: application added, minor changes otherwise; to appear in the Journal of Algebra

Scientific paper

The global Okounkov body of a projective variety is a closed convex cone that encodes asymptotic information about every big line bundle on the variety. In the case of a rank two toric vector bundle E on a smooth projective toric variety, we use its Klyachko filtrations to give an explicit description of the global Okounkov body of P(E). In particular, we show that this is a rational polyhedral cone and that P(E) is a Mori dream space.

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