Hodge decomposition for Kato manifolds

Abstract

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.

arXiv comment24 pages