The Bogomolov-Beauville-Yau decomposition for klt projective varieties with trivial first Chern class - without tears

Abstract

We give a simplified proof (in characteristic zero) of the decomposition theorem for connected complex projective varieties with klt singularities and a numerically trivial canonical bundle. The proof mainly consists in reorganizing some of the partial results obtained by many authors and used in the previous proof but avoids those in positive characteristic by S. Druel. The single, to some extent new, contribution is an algebraicity and bimeromorphic splitting result for generically locally trivial fibrations with fibers without holomorphic vector fields. We first give the proof in the easier smooth case, following the same steps as in the general case, treated next. The last two words of the title are plagiarized from [4].