1999/02/26 by Thomas Peternell, Peternell, Thomas · 2 citations
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.math/9902149
openalex publication_date 1999/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove abundance for a minimal Kaehler threefold which is not both simple and non-Kummer. Recall that a variety is simple if there is no compact subvariety of positive dimension through a sufficiently general point . Furthermore we prove that a smooth compact Kaehler threefold whose canonical bundle is not nef, carries a contraction unless (possibly) the manifold is simple non-Kummer. It is generally conjectured that simple threefolds must be Kummer.