Hodge decomposition for Kato manifolds

We prove that any Kato manifold satisfies the Hodge decomposition, in the sense that $b_k={\sum }_{p+q=k}{h}^{p,q}$, by relating its cohomology to the corresponding cohomology of its modification data. We give, therefore, more evidence supporting a conjecture of Ornea–Verbitsky stating that compact locally conformally Kähler manifolds satisfy the Hodge decomposition. We further study Bott–Chern and Aeppli cohomology of Kato manifolds, showing that in certain degrees they coincide with Dolbeault cohomology.