K�hlerianity of q-Stein spaces

Coverings of locally conformally Kähler complex spaces

“…This generalizes a result for Kähler spaces, see [10,Theorem 2]. In fact, our proof consists of a careful intermix of the proof of that result with further topological arguments.…”

“…The proof now follows the same broad steps as in [10]. Consider K α ⊂ U α compact sets with α∈A K α = X and choose τ α ∈ C ∞ 0 (V α ), τ α ≥ 0 and τ α equals 1 on a neighborhood of g(K α ).…”

“…In Sect. 4, using the above characterization, we generalize to the locally conformal setting a result by [10] about maps with discrete fibers into Kähler spaces. Specifically, we prove: Theorem 4.1 Let g : X −→ Y be a holomorphic map between complex spaces with discrete fibers and assume (Y , ω, θ) is LCK.…”

Ramified coverings over a complete K�hler space

“…Namely if π is locally semi-finite and Y is Stein, then X is also Stein. On the other hand Vâjâitu [8] proved that if π is a holomorphic map with discrete fibers and Y is Kähler, then X is also Kähler.…”

“…Namely if π is locally semi-finite and Y is Stein, then X is also Stein. On the other hand Vâjâitu [8] proved that if π is a holomorphic map with discrete fibers and Y is Kähler, then X is also Kähler.We consider the case of the local semi-finiteness as the property (A) and the complete Kählerity as the property (B). Throughout this paper all complex spaces are supposed to be reduced and with countable topology.…”