Orbifoldes, variétés spéciales et classification des variétés K\" ahlériennes compactes

Abstract

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 $\kappa =0$, or rationally generated (a weak version of rationally connected).