Mori's orbifold ansatz for orbifold Mori fibrations

Let XX^\partial be a smooth projective effective orbifold with κ(X)=\kappa(X^\partial)=-\infty. An orbifold Mori fibration is a fibration whose general fibers are orbifold rationally chain connected. Mori's orbifold ansatz. Then XX^\partial is birational to a smooth orbifold having an orbifold Mori fibration. This is presented as a generalization of weak abundance in Mori's program and is used to construct canonical special fibrations; its resolution is not established in the supplied text.

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Primary source

Steven S. Y. Lu, “A refined Kodaira dimension and its canonical fibration”, arXiv:math/0211029 (2002).

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