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

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

2004-02-14

arxiv.org/abs/math/0402242v1

Mathematics

Algebraic Geometry

Scientific paper

This text is an introduction to math.AG/0110051 (to appear in Ann. Inst. Fourier), and describes a canonical decomposition of compact K\"ahler 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).

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