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3-Fold Extremal Contractions of Types (IC) and (IIB)

Published online by Cambridge University Press:  17 December 2013

Shigefumi Mori
Affiliation:
RIMS, Kyoto University, Oiwake-cho, Kitashirakawa, Sakyo-ku, Kyoto 606-8502, Japan (mori@kurims.kyoto-u.ac.jp)
Yuri Prokhorov
Affiliation:
Department of Algebra, Faculty of Mathematics, Moscow State University, Vorob'evy Gory, Moscow 117234, Russia Laboratory of Algebraic Geometry, SU-HSE, 7 Vavilova Street, Moscow 117312, Russia (prokhoro@gmail.com)
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Abstract

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Let (X, C) be a germ of a 3-fold X with terminal singularities along an irreducible reduced complete curve C with a contraction f:(X, C) → (Z, o) such that C = f−1 (o)red and −KX is ample. Assume that (X, C) contains a point of type (IC) or (IIB). We complete the classification of such germs in terms of a general member containing C.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2014 

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