Poisson cohomology of holomorphic toric Poisson manifolds. I (Q1732892)

From the abstract: ``A holomorphic toric Poisson manifold is a smooth toric variety equipped with a holomorphic Poisson structure, which is invariant under the torus action. In this paper, we compute the Poisson cohomology groups for all holomorphic toric Poisson structures on $\mathbb{C}P^n$, with the standard Poisson structure on $\mathbb{C}P^n$ as a special case. We also compute the algebraic and the formal Poisson cohomology groups of holomorphic toric Poisson structures on $\mathbb{C}^n$.'' The paper is self-contained and clearly written.