Geodesic
Threefold extremal contractions of type (IIA).~I
Izvestiya. Mathematics , Tome 80 (2016) no. 5, pp. 884-909.

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Let $(X,C)$ be a germ of a threefold $X$ with terminal singularities along an irreducible reduced complete curve $C$ with a contraction $f\colon(X,C)\to(Z,o)$ such that $C=f^{-1}(o)_{\mathrm{red}}$ and $-K_X$ is ample. Assume that $(X,C)$ contains a point of type $(\mathrm{IIA})$ and that a general member $H\in|\mathscr O_X|$ containing $C$ is normal. We classify such germs in terms of $H$.
Keywords: extremal contraction, threefold, extremal curve germ, terminal singularity, sheaf. 
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S. Mori; Yu. G. Prokhorov. Threefold extremal contractions of type (IIA).~I. Izvestiya. Mathematics , Tome 80 (2016) no. 5, pp. 884-909. http://geodesic.mathdoc.fr/item/IM2_2016_80_5_a4/

[3] J. Kollár, S. Mori, “Classification of three-dimensional flips”, J. Amer. Math. Soc., 5:3 (1992), 533–703 | DOI | MR | Zbl

[4] Flips and abundance for algebraic threefolds (Univ. of Utah, Salt Lake City, 1991), Astérisque, 211, ed. J. Kollár, Soc. Math. France, Paris, 1992, 258 pp. | MR | Zbl

[5] S. Mori, “Flip theorem and the existence of minimal models for {$3$}-folds”, J. Amer. Math. Soc., 1:1 (1988), 117–253 | DOI | MR | Zbl

[6] S. Mori, Y. Prokhorov, “On $\mathbb Q$-conic bundles”, Publ. Res. Inst. Math. Sci., 44:2 (2008), 315–369 | DOI | MR | Zbl

[7] S. Mori, Y. Prokhorov, “On $\mathbb {Q}$-conic bundles. III”, Publ. Res. Inst. Math. Sci., 45:3 (2009), 787–810 | DOI | MR | Zbl

[8] S. Mori, Y. Prokhorov, “Threefold extremal contractions of type (IA)”, Kyoto J. Math., 51:2 (2011), 393–438 | DOI | MR | Zbl

[9] S. Mori, Y. Prokhorov, “3-fold extremal contractions of types (IC) and (IIB)”, Proc. Edinb. Math. Soc. (2), 57:1 (2014), 231–252 | DOI | MR | Zbl

[10] M. Reid, “Young person's guide to canonical singularities”, Algebraic geometry, Bowdoin, 1985 (Brunswick, Maine, 1985), Proc. Sympos. Pure Math., 46, Part 1, Amer. Math. Soc., Providence, RI, 1987, 345–414 | MR | Zbl