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arXiv · 1712.07209

Flat affine subvarieties in Oeljeklaus-Toma manifolds

Liviu Ornea·Misha Verbitsky·Victor Vuletescu
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Abstract

The Oeljeklaus-Toma (OT-) manifolds are compact, complex, non-Kahler 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 $K$. 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 non-trivial elements in $U$ are primitive in $K$, then $X$ contains no proper complex subvarieties.

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Liviu Ornea, Misha Verbitsky, Victor Vuletescu. 2018-01-06. Flat affine subvarieties in Oeljeklaus-Toma manifolds. https://doi.org/10.1007/s00209-018-2121-2

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