Oeljeklaus-Toma manifolds admitting no complex subvarieties

Liviu Ornea; Misha Verbitsky

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arXiv · 1009.1101

Oeljeklaus-Toma manifolds admitting no complex subvarieties

Liviu Ornea·Misha Verbitsky

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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 and trivial Chern class. Using this form, we prove that the OT-manifolds admitting a locally conformally Kahler 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 w is Zariski dense.

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BibTeX RIS

Liviu Ornea, Misha Verbitsky. 2011-02-02. Oeljeklaus-Toma manifolds admitting no complex subvarieties. https://arxiv.org/abs/1009.1101

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