Flips in dimension three via crepant descent method
The flip theorem proved by \textit{S. Mori} [J. Am. Math. Soc. 1, No. 1, 117--253 (1988; Zbl 0649.14023)], is one the main breakthrough in the birational classification of projective varieties. Mori's proof is based on a deep analysis of the possible singularities of an anticanonical section of a flipping contraction and relies on \textit{Y. Kawamata}'s results [Ann. Math. (2) 127, No. 1, 93--163 (1988; Zbl 0651.14005)] to conclude from this the existence of flips for 3-folds. In the note under review the author gives an alternative conclusion of the proof. The existence of a general elephant [\textit{J. Kollár} and \textit{S. Mori}, J. Am. Math. Soc. 5, No. 3, 533--703 (1992; Zbl 0773.14004)], reduces the existence of flips to the existence of log flops. The latter are proved to exist by descending induction on the number of crepant divisors via the study of terminal extractions.
scientific article; zbMATH DE number 2024719
scientific article