Curves on Oeljeklaus-Toma Manifolds
Sima Verbitsky
TL;DR
This paper proves that Oeljeklaus-Toma manifolds, a class of complex non-Kähler manifolds constructed from number fields, do not contain any compact complex curves, highlighting a key geometric property.
Contribution
The paper establishes that Oeljeklaus-Toma manifolds contain no compact complex curves, extending understanding of their complex geometric structure.
Findings
Oeljeklaus-Toma manifolds contain no compact complex curves
Generalization of properties from Inoue surfaces to higher dimensions
Insight into the complex geometry of non-Kähler manifolds
Abstract
Oeljeklaus-Toma manifolds are complex non-K\"ahler manifolds constructed by Oeljeklaus and Toma from certain number fields, and generalizing the Inoue surfaces . We prove that Oeljeklaus-Toma manifolds contain no compact complex curves.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Algebraic Geometry and Number Theory