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Non-Kähler compact complex manifolds associated to number fields

Karl Oeljeklaus, Matei Toma (2005)

Annales de l’institut Fourier

For algebraic number fields K with s > 0 real and 2 t > 0 complex embeddings and “admissible” subgroups U of the multiplicative group of integer units of K we construct and investigate certain ( s + t ) -dimensional compact complex manifolds X ( K , U ) . We show among other things that such manifolds are non-Kähler but admit locally conformally Kähler metrics when t = 1 . In particular we disprove a conjecture of I. Vaisman.

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