A reduction map for nef line bundles
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In a recent preprint, H. Tsuji gave a number of interesting assertions on the structure of pseudo-effective line bundles on projective manifolds. In particular, he postulated the existence of an almost-holomorphic "reduction map", whose fibers are maximal subvarieties on which the line bundle is numerically trivial.
The purpose of this note is to give a simple, algebraic proof of the existence of a reduction map in the case where the line bundle is nef.