2004/02/14 by Frédéric Campana, Frederic Campana, Campana, Frederic
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.AG #math.CV
paper · pdf · doi:10.48550/arxiv.math/0402242
arxiv created 2004/02/14 · openalex publication_date 2004/02/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This text is an introduction to math.AG/0110051 (to appear in Ann. Inst. Fourier), and describes a canonical decomposition of compact Kähler manifolds X first by means of their "core", the unique fibration on X with fibres special, and orbifold base of general type. Being special means that there does not exist a fibration onto an orbifold of general type. The core is next decomposed into a tower of fibrations with all orbifold fibres either with κ=0, or rationally generated (a weak version of rationally connected).