Flat affine subvarieties in Oeljeklaus-Toma manifolds

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.

12 pages, v. 2.0, changed the title to avoid confusion with an earlier paper

References in corpus (1)

• Oeljeklaus-Toma manifolds and arithmetic invariants

Cited by in corpus (2)

• Algebraic dimension and complex subvarieties of hypercomplex nilmanifolds
• The continuity equation for Hermitian metrics: Calabi estimates, Chern scalar curvature and Oeljeklaus-Toma manifolds