On Fano–Enriques threefolds
Sbornik. Mathematics, Tome 198 (2007) no. 4, pp. 559-574 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $U\subset \mathbb P^N$ be a projective variety that is not a cone and whose hyperplane sections are smooth Enriques surfaces. It is proved that the degree of such $U$ is at most 32 and this bound is sharp. Bibliography: 16 titles.
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Yu. G. Prokhorov. On Fano–Enriques threefolds. Sbornik. Mathematics, Tome 198 (2007) no. 4, pp. 559-574. http://geodesic.mathdoc.fr/item/SM_2007_198_4_a5/

[1] G. Fano, “Sulle varieta algebriche a tre dimensioni le cui sezioni iperpiane sono superficie di genere zero e bigenere uno”, Mem. Mat. Sci. Fis. Natur. Soc. Ital. Sci. (3), 24 (1938), 41–66 | Zbl

[2] L. Godeaux, “Sur les variétés algébriques à trois dimensions dont les sections hyperplanes sont des surfaces de genres zéro et de bigenre un”, Acad. Roy. Belg. Bull. Cl. Sci. (5), 14 (1933), 134–140 | Zbl

[3] A. Conte, “Two examples of algebraic threefolds whose hyperplane sections are Enriques surfaces”, Algebraic geometry – open problems (Ravello, 1982), Lecture Notes in Math., 997, Springer-Verlag, Berlin, 1983, 124–130 | DOI | MR | Zbl

[4] A. Conte, J. P. Murre, “Algebraic varieties of dimension three whose hyperplane sections are Enriques surfaces”, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 12:1 (1985), 43–80 | MR | Zbl

[5] L. Bayle, “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

[6] T. Sano, “On classifications of non-Gorenstein $\mathbf Q$-Fano 3-folds of Fano index 1”, J. Math. Soc. Japan, 47:2 (1995), 369–380 | DOI | MR | Zbl

[7] T. Minagawa, “Deformations of $\mathbb Q$-Calabi–Yau 3-folds and $\mathbb Q$-Fano 3-folds of Fano index 1”, J. Math. Sci. Univ. Tokyo, 6:2 (1999), 397–414 | MR | Zbl

[8] I. A. Cheltsov, “Osobennosti trekhmernykh mnogoobrazii, obladayuschikh obilnym effektivnym divizorom – gladkoi poverkhnostyu kodairovoi razmernosti nul”, Matem. zametki, 59:4 (1996), 618–626 | MR | Zbl

[9] Yu. G. Prokhorov, “Stepen trekhmernykh mnogoobrazii Fano s kanonicheskimi gorenshteinovymi osobennostyami”, Matem. sb., 196:1 (2005), 81–122 | MR | Zbl

[10] J. Kollár (ed.), Flips and abundance for algebraic threefolds, Papers from the Second Summer Seminar on Algebraic Geometry (University of Utah, Salt Lake City, Utah, 1991), Astérisque, 211, Soc. Math. France, Paris, 1992 | MR | Zbl

[11] P. Jahnke, I. Radloff, “Gorenstein Fano threefolds with base points in the anticanonical system”, Compos. Math., 142:2 (2006), 422–432 | DOI | MR | Zbl

[12] V. V. Przhiyalkovskii, I. A. Cheltsov, K. A. Shramov, “Giperellipticheskie i trigonalnye trekhmernye mnogoobraziya Fano”, Izv. RAN. Ser. matem., 69:2 (2005), 145–204 | MR | Zbl

[13] J. Kollár, S. Mori, Birational geometry of algebraic varieties, Cambridge Tracts in Math., 134, Cambridge Univ. Press, Cambridge, 1998 | MR | Zbl

[14] F. R. Cossec, I. V. Dolgachev, Enriques surfaces. I, Progr. Math., 76, Birkhäuser, Boston, MA, 1989 | MR | Zbl

[15] T. Sano, “Classification of non-Gorenstein $\mathbf Q$-Fano $d$-folds of Fano index greater than $d-2$”, Nagoya Math. J., 142 (1996), 133–143 | MR | Zbl

[16] V. A. Iskovskikh, “Minimalnye modeli ratsionalnykh poverkhnostei nad proizvolnymi polyami”, Izv. AN SSSR. Ser. matem., 43:1 (1979), 19–43 ; V. A. Iskovskih, “Minimal models of rational surfaces over arbitrary fields”, Math. USSR-Izv., 14:1 (1980), 17–39 | MR | Zbl | DOI | Zbl