Mathematical Research Letters

Volume 18 (2011)

Number 4

Oeljeklaus–Toma Manifolds Admitting No Complex Subvarieties

Pages: 747 – 754



Liviu Ornea (University of Bucharest, Faculty of Mathematics, Bucharest, Romania and, Institute of Mathematics 'Simion Stoilow' of the Romanian Academy, Bucharest, Romania)

Misha Verbitsky (and Laboratory of Algebraic Geometry, Moscow, 117312, Russia)


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.

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