Algebra & Number Theory
- Algebra Number Theory
- Volume 6, Number 5 (2012), 995-1017.
Cox rings and pseudoeffective cones of projectivized toric vector bundles
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 .
Algebra Number Theory, Volume 6, Number 5 (2012), 995-1017.
Received: 7 October 2010
Revised: 20 September 2011
Accepted: 21 December 2011
First available in Project Euclid: 20 December 2017
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 14C20: Divisors, linear systems, invertible sheaves
Secondary: 14J60: Vector bundles on surfaces and higher-dimensional varieties, and their moduli [See also 14D20, 14F05, 32Lxx] 14M25: Toric varieties, Newton polyhedra [See also 52B20] 14L30: Group actions on varieties or schemes (quotients) [See also 13A50, 14L24, 14M17]
González, José; Hering, Milena; Payne, Sam; Süß, Hendrik. Cox rings and pseudoeffective cones of projectivized toric vector bundles. Algebra Number Theory 6 (2012), no. 5, 995--1017. doi:10.2140/ant.2012.6.995. https://projecteuclid.org/euclid.ant/1513729843