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# Mathematical Research Letters

## Volume 18 (2011)

### Number 4

### Oeljeklaus–Toma Manifolds Admitting No Complex Subvarieties

Pages: 747 – 754

DOI: http://dx.doi.org/10.4310/MRL.2011.v18.n4.a12

#### Authors

#### Abstract

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.