Compact K" ahler threefolds of π₁-general type

2004/02/14 by F. Campana, Q. Zhang, Campana, F. +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #math.AG

paper · pdf · doi:10.48550/arxiv.math/0402241

openalex publication_date 2004/02/14 · arxiv created 2004/05/14 · arxiv updated 2009/12/01 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

We classify these threefolds, which are the ones such that their universal cover is not compact and not covered by positive-dimensional compact analytic subsets. We show that these threefolds have nonnegative Kodaira dimension, and that their Iitaka-Moishezon fibrations are, after a suitable finite etale cover, bimeromorphic to a submersion with fibres complex tori, and base of general type and π₁-general type.

Related

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• Subadditivity of Kodaira dimensions for fibrations of three-folds in positive characteristics
• Iitaka's C_n,m conjecture for 3-folds in positive characteristic
• A refined Kodaira dimension and its canonical fibration
• Crepant resolutions of Weierstrass threefolds and non-Kodaira fibres