Kyoto Journal of Mathematics

Threefold extremal contractions of type (IA)

Shigefumi Mori and 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)(Z,o) such that C=f1(o)red and KX is ample. Assume that a general member F|KX| 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|OX| containing C.

Article information

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

Dates
First available in Project Euclid: 22 April 2011

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1303494508

Digital Object Identifier
doi:10.1215/21562261-1214393

Mathematical Reviews number (MathSciNet)
MR2793273

Zentralblatt MATH identifier
1230.14017

Subjects
Primary: 14J30: $3$-folds [See also 32Q25] 14E 14E30: Minimal model program (Mori theory, extremal rays)

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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