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arXiv · 1004.4188

Threefold extremal contractions of type IA

Shigefumi Mori·Yuri Prokhorov
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Abstract

Let $(X,C)$ be a germ of a threefold $X$ with terminal singularities along an irreducible reduced complete curve $C$ with a contraction $f: (X,C)\to (Z,o)$ such that $C=f^{-1}(o)_{\red}$ and $-K_X$ is ample. Assume that a general member $F\in |-K_X|$ meets $C$ only at one point $P$ and furthermore $(F,P)$ is Du Val of type A if index$(X,P)=4$. We classify all such germs in terms of a general member $H\in |O_X|$ containing $C$.

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Shigefumi Mori, Yuri Prokhorov. 2010-04-23. Threefold extremal contractions of type IA. https://doi.org/10.1215/21562261-1214393

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