Geodesic
Birational geometry of toric 3-folds
Izvestiya. Mathematics, Tome 21 (1983) no. 2, pp. 269-280 
V. I. Danilov. Birational geometry of toric 3-folds. Izvestiya. Mathematics, Tome 21 (1983) no. 2, pp. 269-280. http://geodesic.mathdoc.fr/item/IM2_1983_21_2_a2/
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     title = {Birational geometry of toric 3-folds},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The following result is proved. Suppose given smooth toric $3$-folds $X$ and $Y$ and a proper birational toric morphism $f\colon X\to Y$. Then $f$ decomposes as a composite of blow-ups and blow-downs in smooth toric strata. Bibliography: 7 titles.

[1] Khironaka X., “Razreshenie osobennostei algebraicheskikh mnogoobrazii nad polyami kharakteristiki nul”, Matematika, 9:6 (1965), 2–70

[2] Kempf G., Knudsen F., Mumford D., Saint-Donat B., Toroidal embedding. I, Lect. Notes in Math., 339, 1973 | MR | Zbl

[3] Oda T., Lecture on torus embeddings and applications. Tata Inst. Fund. Research, Springer-Verlag, Bombay, 1978 | MR

[4] Danilov V. I., “Geometriya toricheskikh mnogoobrazii”, Uspekhi matem. nauk, 33:2 (1974), 85–134 | MR

[5] Reid M., “Canonical 3-fold”, Proceedings of the Journees de Géométrie Algébrique, Anger, 1979, 273–310 | MR

[6] Frumkin M. A., “Opisanie elementarnykh trekhmernykh mnogogrannikov”, I Vsesoyuznoe soveschanie po statisticheskomu i diskretnomu analizu nechislovoi informatsii, ekspertnym otsenkam i diskretnoi optimizatsii (tezisy dokladov), Moskva, Alma-Ata, 1981

[7] White G. K., “Lattice tetrahedra”, Canad. J. Math., 16:2 (1964), 389–397 | MR