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Article

Flat affine subvarieties in Oeljeklaus–Toma manifolds

Mathematische Zeitschrift. 2018. P. 1-9.
Verbitsky M., Vuletescu V., Ornea L.

The Oeljeklaus–Toma (OT-)manifolds are compact, complex, non-Kähler manifolds constructed by Oeljeklaus and Toma, and generalizing the Inoue surfaces. Their construction uses the number-theoretic data: a number field K and a torsion-free subgroup U in the group of units of the ring of integers of K, with rank of U equal to the number of real embeddings of K. OT-manifolds are equipped with a torsion-free flat affine connection preserving the complex structure (this structure is known as “flat affine structure”). We prove that any complex subvariety of smallest possible positive dimension in an OT-manifold is also flat affine. This is used to show that if all elements in U∖{1} are primitive in K, then X contains no proper analytic subvarieties.