Oeljeklaus-Toma manifolds admitting no complex subvarieties

Details Oeljeklaus-Toma manifolds admitting no complex subvarieties Oeljeklaus-Toma manifolds admitting no complex subvarieties

2010-09-06

arxiv.org/abs/1009.1101v5

Math. Res. Lett. 18 (2011), no. 04, 747-754

Mathematics

Complex Variables

11 pages; no changes from the previous submission, which was the same file submitted twice by an error

Scientific paper

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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