Flips from semi-stable 4-folds whose degenerate fibers are unions of Cartier divisors which are terminal factorial 3-folds

Abstract

We shall investigate flipping contractions from a semi-stable 4-fold $X$ whose degenerate fiber is a union of Cartier divisors which are terminal factorial 3-folds. Especially we shall prove that $X$ is smooth along the flipping locus, and that the flip exists for such contractions.