Mathematical Research Letters
Volume 18 (2011)
Oeljeklaus–Toma Manifolds Admitting No Complex Subvarieties
Pages: 747 – 754
The Oeljeklaus–Toma (OT)-manifolds are complex manifolds constructed by Oeljeklaus and Toma from certain number fields, and generalizing the Inoue surfaces $S_m$. On each OT-manifold we construct a holomorphic line bundle with semipositive curvature form $\omega_0$ and trivial Chern class. Using this form, we prove that the OT-manifolds admitting a locally conformally Kähler structure have no non-trivial complex subvarieties. The proof is based on the Strong Approximation theorem for number fields, which implies that any leaf of the null-foliation of $\omega_0$ is Zariski dense.