Cox rings and pseudoeffective cones of projectivized toric vector bundles (bibtex)

Abstract:

We study projectivizations of a special class of toric vector bundles that includes cotangent bundles, whose associated Klyachko filtrations are parti cularly simple. For these projectivized bundles, we give generators for the cone of effective divisors and a presentation of the Cox ring as a polynomial algebr a 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 projectiviz ed toric vector bundles whose Cox rings are isomorphic to that of \bar M_0n.

Reference:

Cox rings and pseudoeffective cones of projectivized toric vector bundles (Jose Gonzalez, Milena Hering, Sam Payne, Hendrik Süß), Algebra & Number Theory, volume 6, 2012.

Bibtex Entry:

@article{coxBUndle, author = {{Gonzalez}, Jose and {Hering}, Milena and {Payne}, Sam and {S{\"u}{\ss}}, Hendrik }, title = "{Cox rings and pseudoeffective cones of projectivized toric vector bundles}", journal = {Algebra \& Number Theory}, archivePrefix = "arXiv", eprint = {1009.5238}, primaryClass = "math.AG", keywords = {Mathematics - Algebraic Geometry, 14C20, 14J60, 14M25 14L30}, year = 2012, volume = 6, number = 5, doi= {10.2140/ant.2012.6.995}, url = {http://arxiv.org/abs/1009.5238}, gsid = {2146266613142647124}, abstract={We study projectivizations of a special class of toric vector bundles that includes cotangent bundles, whose associated Klyachko filtrations are parti cularly simple. For these projectivized bundles, we give generators for the cone of effective divisors and a presentation of the Cox ring as a polynomial algebr a 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 projectiviz ed toric vector bundles whose Cox rings are isomorphic to that of \bar M_0n. }, }

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