Positivity properties of divisors on Toric Vector Bundles (2308.09014v1)

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.