Algebraicity under bijective morphisms and nonprojective varieties (Q1057405)

It is proved that algebraicity of compact complex spaces is invariant under topological holomorphic maps. For any field of characteristic zero an example of a Cohen-Macaulay scheme X is given which has only trivial line bundles and admits only constant maps to smooth varieties while the normalization \({\mathbb{P}}_ 2(k)\to X\) is bijective.