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Cox
rings and pseudoeffective cones of projectivized toric vector
bundles
José González, Milena Hering, Sam Payne and Hendrik Süß |
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Vol. 6 (2012), No. 5, 995–1017
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Abstract |
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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 M0,n. |
Keywords
Cox ring, pseudoeffective cone, toric vector bundle, Mori
dream space, torus quotient, Losev–Manin moduli space,
Deligne–Mumford moduli space, iterated blow up
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Mathematical Subject Classification 2010
Primary: 14C20
Secondary: 14J60, 14M25, 14L30
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Milestones
Received: 7 October 2010
Revised: 20 September 2011
Accepted: 21 December 2011
Published: 31 July 2012
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Authors |
| José González | |
| Department of Mathematics The University of British Columbia Room 125, 1984 Mathematics Road Vancouver BC V6T 1Z2 Canada |
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| Milena Hering | |
| Department of Mathematics University of Connecticut 196 Auditorium Road, Unit 3009 Storrs, CT 06269-3009 United States |
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| Sam Payne | |
| Mathematics Department Yale University 10 Hillhouse Ave. New Haven, CT 06511 United States |
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| http://www.math.yale.edu/~sp547/ | |
| Hendrik Süß | |
| Lehrstuhl für Algebra und
Geometrie BTU Cottbus Postfach 10 13 44 D-03013 Cottbus Germany |
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| http://www.math.tu-cottbus.de/~suess | |
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