Geodesic
Smoothness of the general anticanonical divisor on a Fano 3-fold
Izvestiya. Mathematics, Tome 14 (1980) no. 2, pp. 395-405 
V. V. Shokurov. Smoothness of the general anticanonical divisor on a Fano 3-fold. Izvestiya. Mathematics, Tome 14 (1980) no. 2, pp. 395-405. http://geodesic.mathdoc.fr/item/IM2_1980_14_2_a10/
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     title = {Smoothness of the general anticanonical divisor on {a~Fano} 3-fold},
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Voir la notice de l'article provenant de la source Math-Net.Ru

Smoothness of the general anticanonical divisor of a Fano 3-fold is proved. In addition, an analogous result is established for the linear system $|\mathscr H|$, where $r\mathscr H\sim-K_V$ for some natural number $r$. The results obtained in the paper can be used to investigate projective imbeddings of Fano 3-folds. Bibliography: 6 titles.

[1] Bertini E., Introduzione alia geometria proiettiva degli iperspazi, 2 ed., Messina, 1923

[2] Bombieri E., “Canonical models of surfaces of general type”, Publications Mathematiques, 1973, no. 42, 447–495 | MR

[3] Fujita T., “Defining equations for certain types of polarized varieties”, Compl. Anal. and Alg. Geomet., Iwanami Shoten, 1977, 165–173 | MR

[4] Iskovskikh V. A., “Trekhmernye mnogoobraziya Fano, I”, Izv. AN SSSR. Ser. matem., 41 (1977), 516–562 | MR | Zbl

[5] Mumford D., “Pathologies, III”, Amer. J. Math., 89 (1967), 94–104 | DOI | MR | Zbl

[6] Saint-Donat B., “Projective models of K3 surfaces”, Amer. J. Math., 96:4 (1974), 602–639 | DOI | MR | Zbl