Mathematics – Complex Variables
Scientific paper
2010-09-06
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.
Ornea Liviu
Verbitsky Misha
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