Positivity properties of divisors on Toric Vector Bundles

2023/08/17 by George, Courtney, Manon, Christopher
#05E10 #13A50 #14M25 #14T05 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2308.09014

Abstract

We use presentations of the Cox rings of projectivized toric vector bundles and elements of matroid theory to compute Newton-Okounkov bodies, effective cones, and nef cones of these spaces. As an application we analyze the Fano property and establish Fujita's freeness and ampleness conjectures for several classes of projectivized toric vector bundles.

Related

• Some positivity results for toric vector bundles
• Algebra and Geometry of Irreducible toric vector bundles of rank n on ℙⁿ
• Okounkov bodies on projectivizations of rank two toric vector bundles
• Arithmetic positivity on toric varieties
• Projectivized rank two toric vector bundles are Mori dream spaces