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We give a simplified proof (in characteristic zero) of the decompositiontheorem for complex projective varieties with klt singularities and numericallytrivial canonical bundle. The proof rests in an essential way on most of thepartial results of the previous proof obtained by many authors, but avoidsthose in positive characteristic by S. Druel. The single to some extent newcontribution is an algebraicity and bimeromorphic splitting result forgenerically locally trivial fibrations with fibres without holomorphic vectorfields. We give first the proof in the easier smooth case, following the samesteps as in the general case, treated next.

The Bogomolov-Beauville-Yau Decomposition for Klt Projective Varieties with Trivial First Chern Class -Without Tears-