Smoothness, Semistability, and Toroidal Geometry

0.2. Structure of the proof. 1. As in [dJ], we choose a projection X 99K P of relative dimension 1, and apply semistable reduction to obtain a model X ′ → B over a suitable Galois base change B → P , with Galois group G. 2. We apply induction on the dimension to B , therefore we may assume that B is smooth, and that the discriminant locus of X ′ → B is a G-strict divisor of normal crossings. 3. A few auxiliary blowups make the quotient X /G toroidal. 4. Theorem 11* of [KKMS] about toroidal resolutions finishes the argument.