Boundedness of non-birational extremal contractions

Abstract

We consider $K_X$-negative extremal contractions $f:X\to (Z,o)$, where $X$ is an algebraic threefold with only $\epsilon$-log terminal Q-factorial singularities and $(Z,o)$ is a two (resp., one)-dimensional germ. The main result is that $K_X$ is 1, 2, 3, 4 or 6-complementary or we have, so called, exceptional case and then the singularity $(Z\in o)$ is bounded (resp., the multiplicity of the central fiber $f^{-1}(o)$ is bounded).

21 pages. LaTeX2e, some errors corrected, submited to Internat. J. Math

Cited by in corpus (4)

• Log canonical $3$-fold complements
• Strong $(\delta ,n)$-complements for semi-stable morphisms
• Complements on log surfaces
• On classification of Mori contractions: Elliptic curve case