On the Bimeromorphic Geometry of Compact Complex Contact Threefolds

Abstract

We prove that a compact contact threefold which is bimeromorphically equivalent to a Kaehler manifold and not rationally connected is the projectivised tangent bundle of a Kaehler surface.

LaTeX, 11 pages, final version (Theorem 2.5 fixed); to appear in a volume on the occasion of the conference "Classification of algebraic varieties" in Schiermonnikoog 2009