Geodesic
On the resolution of 3-dimensional terminal singularities
Matematičeskie zametki, Tome 77 (2005) no. 1, pp. 127-140.

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We show that there is at most one nonrational exceptional divisor with discrepancy 1 over a three-dimensional terminal point of type $cD$. If such a divisor exists, then it is birationally isomorphic to the surface $\mathbb P^1\times C$, where $C$ is a hyperelliptic (for $g(C)>1$) curve. 
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D. A. Stepanov. On the resolution of 3-dimensional terminal singularities. Matematičeskie zametki, Tome 77 (2005) no. 1, pp. 127-140. http://geodesic.mathdoc.fr/item/MZM_2005_77_1_a11/

[1] Reid M., “Minimal models of canonical $3$-folds”, Algebraic Varieties and Analytic Varieties, Adv. Studies in Pure Math., 1, Kinokuniya; North-Holland, 1983, 131–180 | MR

[2] Mori S., “On $3$-dimensional terminal singularities”, Nagoya Math. J., 98 (1985), 43–66 | MR | Zbl

[3] Kollár J., Shepard-Barron N., “Threefolds and deformations of surface singularities”, Invent. Math., 91 (1988), 299–338 | DOI | MR | Zbl

[4] Iskovskikh V. A., “Osobennosti na minimalnykh modelyakh algebraicheskikh mnogoobrazii”, Tr. sem. pod rukovodstvom I. R. Shafarevicha, 1996–1998, M., 1998, 41–61

[5] Reid M., “Young person's guide to canonical singularities”, Proc. Symp. Pure Math., 46:1 (1987), 345–414 | MR | Zbl

[6] Reid M., “Canonical $3$-folds”, Jornées de Géométrie Algébrique d'Angers, ed. A. Beauville, Sijthoff; Noordhoff, Alpen aan den Rijn, 1980, 273–310 | MR

[7] Prokhorov Yu. G., “Zamechanie o razreshenii trekhmernykh terminalnykh osobennostei”, UMN, 57:4 (2002), 187–188 | MR | Zbl

[8] Markushevich D. G., “Kanonicheskie osobennosti trekhmernykh giperpoverkhnostei”, Izv. AN SSSR. Ser. matem., 49 (1985), 334–368 | MR | Zbl

[9] Prokhorov Yu. G., “$\mathbb E1$-blowing ups of terminal singularities”, J. Math. Sci., 115:3 (2003), 2395–2427 | DOI | Zbl

[10] Hayakawa T., “Blowing ups of $3$-dimensional terminal singularities”, Publ. RIMS. Kyoto Univ., 35 (1999), 515–570 | DOI | MR | Zbl

[11] Markushevich D., “Minimal discrepancy for a terminal $cDV$ singularity is $1$”, J. Math. Sci. Univ. Tokyo, 3 (1996), 445–456 | MR | Zbl

[12] Arnold V. I., Varchenko A. N., Gusein-Zade S. M., Osobennosti differentsiruemykh otobrazhenii, Nauka, M., 1982 | MR