Curvature on some Kähler toric manifolds

We use the Guillemin–Abreu formalism to give a unified treatment of Kähler metrics with positive holomorphic bisectional curvature on ${\mathbb{C}}^n$ and positive holomorphic sectional curvature on $\mathcal{O}(-\mathrm{\ell })$ and the Hirzebruch manifolds $M_{n,\mathrm{\ell }}$.