Boundedness of non-birational extremal contractions

Details Boundedness of non-birational extremal contractions Boundedness of non-birational extremal contractions

1999-01-02

arxiv.org/abs/math/9901004v3

Internat. J. Math., 11(3):393- 411, 2000

Mathematics

Algebraic Geometry

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

Scientific paper

We consider $K_X$-negative extremal contractions $f\colon X\to (Z,o)$, 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).

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