Cox rings and pseudoeffective cones of projectivized toric vector bundles

Details Cox rings and pseudoeffective cones of projectivized toric vector bundles Cox rings and pseudoeffective cones of projectivized toric vector bundles

2010-09-27

arxiv.org/abs/1009.5238v2

Mathematics

Algebraic Geometry

20 pages. v2: Revised and expanded, treating a larger class of toric vector bundles and giving new examples whose Cox rings ar

Scientific paper

We study projectivizations of a special class of toric vector bundles that includes cotangent bundles, whose associated Klyachko filtrations are particularly simple. For these projectivized bundles, we give generators for the cone of effective divisors and a presentation of the Cox ring as a polynomial algebra over the Cox ring of a blowup of a projective space along a sequence of linear subspaces. As applications, we show that the projectivized cotangent bundles of some toric varieties are not Mori dream spaces and give examples of projectivized toric vector bundles whose Cox rings are isomorphic to that of M_{0,n}.

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