Toric Kato manifolds

We introduce and study a special class of Kato manifolds, which we call toric manifolds. Their construction stems from geometry, as their universal covers are open subsets algebraic varieties non-finite type. This generalizes previous constructions Tsuchihashi Oda, in complex dimension 2, retrieves the properly blown-up Inoue surfaces. topological analytical properties manifolds link certain invariants to natural combinatorial data coming construction. Moreover, produce families flat degenerations any manifold, serve an essential tool computing Hodge numbers. In last part, Hermitian geometry give characterization result for existence locally conformally Kähler metrics on manifold. Finally, prove that no manifold carries balanced large ≥3 do not support pluriclosed metrics.