Cox rings of projectivized toric vector bundles and toric flag Bundles
Courtney George, Christopher Manon

TL;DR
This paper investigates when projectivized toric vector bundles and their natural algebraic operations are Mori dream spaces, using Cox rings and flag bundles to analyze their properties and provide explicit examples.
Contribution
It introduces criteria for when direct sums of toric vector bundles preserve the Mori dream space property, linking this to associated flag bundles and Cox ring computations.
Findings
Criteria for direct sum bundles to be Mori dream spaces
Explicit Cox ring presentation for the full flag bundle of tangent space
Examples illustrating the relationship between vector bundle operations and Mori dream space status
Abstract
Work of Gonz\'alez, Hering, Payne, and S\"uss shows that it is possible to find both examples and non-examples of Mori dream spaces among projectivized toric vector bundles. This result, and the combinatorial nature of the data of projectivized toric vector bundles make them an ideal test class for the question: what makes a variety a Mori dream space? In the present paper we consider this question with respect to natural algebraic operations on vector bundles. Suppose is a toric vector bundle such that the projectivization is a Mori dream space, then when are the direct sum bundles , also Mori dream spaces? We give an answer to this question utilizing a relationship with the associated full flag bundle . We…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic Geometry and Number Theory · Commutative Algebra and Its Applications
