On algebraic threefolds whose hyperplane sections are Enriques surfaces
Sbornik. Mathematics, Tome 186 (1995) no. 9, pp. 1341-1352 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper the following problem is solved: given a singular Fano variety $X$, find a smooth Enriques surface which is an ample Cartier divisor on $X$. The results obtained enable one to construct, using singular Fano varieties, examples of threefolds whose hyperplane sections are Enriques surfaces. They can be used in the classification of log-Fano varieties of (Fano) index 1.
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     title = {On algebraic threefolds whose hyperplane sections are {Enriques} surfaces},
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Yu. G. Prokhorov. On algebraic threefolds whose hyperplane sections are Enriques surfaces. Sbornik. Mathematics, Tome 186 (1995) no. 9, pp. 1341-1352. http://geodesic.mathdoc.fr/item/SM_1995_186_9_a6/

[1] Alexeev V. A., “Theorems about good divisors on log-Fano varieties”, Lect. Notes in Math., 1479, 1989, 1–9 | MR

[2] Bayle L., “Classification des variétés complexes projectives de dimension trois dont une section hyperplane générale est une surface d'Enriques”, J. Reine Angew Math., 449 (1994), 9–63 | MR | Zbl

[3] Blache R., The structure of l.c. surfaces of Kodaira dimension zero, I, Preprint, 1992 | MR | Zbl

[4] Klemens Kh., Kollar Ya., Mori S., Mnogomernaya kompleksnaya geometriya, Mir, 1993

[5] Cossec F., “Projective models of Enriques surfaces”, Math. Ann., 265 (1983), 283–334 | DOI | MR | Zbl

[6] Conte A., “Two examples of algebraic threefolds whose hyperplane sections are Enriques surfaces”, Open Problems, Proceedings, Ravello, Lect. Notes in Math., 997, 1982, 124–130 | MR

[7] Conte A., Murre J. P., “Algebraic varieties of dimension three whose hyperplane sections are Enriques surfaces”, Annali della Souola Normale Sup. de Pisa, 12 (1985), 43–80 | MR | Zbl

[8] Conte A., Murre J. P., “On the definition and on the nature of the singularities of Fano threefolds”, Rend. Semin. Mat. Univ. e Politech. Torino, 44 (1986), 51–67 | MR

[9] Fano G., “Sulle varrietà algebriche a tre dimensioni le cui sezioni iperpiane sono superficie di genere zero e bigenere uno”, Memorie società dei XL, 24 (1938), 41–66 | Zbl

[10] Godeaux L., “Sur les variétés algébriques à trois dimensions dont les sections hyperplanes sont des surfaces de genre zéro et bigenre un”, Bull. Acad. Belgique. Cl. des Sci., 14 (1933), 134–140

[11] Kawamata Y.,Matsuda K.,Matsuki K., “Introduction to the minimal model program”, Algebraic Geometry, Sendai, Adv. Stud. in Pure Math., 10, 1987, 283–360 | MR | Zbl

[12] Miyaoka Y., Mori S., “A numerical criterion for uniruledness”, Ann. Math., 124 (1986), 65–69 | DOI | MR | Zbl

[13] Reid M., Projective morphism according to Kawamata, Preprint, 1983

[14] Prokhorov Yu. G., “Invariantnye podmnogoobraziya v prostranstvakh binarnykh form”, Algebra i analiz, 4:5 (1992), 172–180 | MR | Zbl

[15] Sano T., Classification of $Q$-Fano threefolds of Fano index 1 with non-Gorenstein singularities, Preprint, 1993

[16] Shokurov V. V., “Gladkost obschego antikanonicheskogo divizora na mnogoobraziyakh Fano”, Izv. AN SSSR. Ser. matem., 43:2 (1979), 430–441 | MR | Zbl

[17] Shin K.-H., “3-dimensional Fano varieties with canonical singularities”, Tokyo J. Math., 12 (1989), 375–385 | MR | Zbl

[18] Zhang D.-Q., “Logarithmic Enriques surfaces”, J. Math. Kyoto Univ., 31-2 (1991), 419–466 | MR | Zbl