On the Bimeromorphic Geometry of Compact Complex Contact Threefolds

TL;DR

This paper proves that certain compact complex contact threefolds, which are bimeromorphically related to Kaehler manifolds and not rationally connected, are actually projectivised tangent bundles of Kaehler surfaces.

Contribution

It establishes a classification result linking bimeromorphic equivalence, contact structures, and the geometry of Kaehler surfaces.

Findings

Contact threefolds bimeromorphic to Kaehler manifolds are projectivised tangent bundles.

Non-rationally connected contact threefolds have a specific geometric structure.

Provides a classification of these complex 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.