Kyoto Journal of Mathematics

Threefold extremal contractions of type (IA)

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 $C=f^{-1}(o)_{\operatorname {red}}$ and $-K_{X}$ is ample. Assume that a general member $F\in |-K_{X}|$ meets $C$ only at one point $P$, and furthermore assume that $(F,P)$ is Du Val of type A if index $(X,P)=4$. We classify all such germs in terms of a general member $H\in |\mathscr {O}_{X}|$ containing $C$.

Article information

Source
Kyoto J. Math., Volume 51, Number 2 (2011), 393-438.

Dates
First available in Project Euclid: 22 April 2011

https://projecteuclid.org/euclid.kjm/1303494508

Digital Object Identifier
doi:10.1215/21562261-1214393

Mathematical Reviews number (MathSciNet)
MR2793273

Zentralblatt MATH identifier
1230.14017

Citation

Mori, Shigefumi; Prokhorov, Yuri. Threefold extremal contractions of type (IA). Kyoto J. Math. 51 (2011), no. 2, 393--438. doi:10.1215/21562261-1214393. https://projecteuclid.org/euclid.kjm/1303494508

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