Geodesic
The degree of $\mathbb Q$-Fano threefolds
Sbornik. Mathematics, Tome 198 (2007) no. 11, pp. 1683-1702 Cet article a éte moissonné depuis la source Math-Net.Ru

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We prove that the degree of three-dimensional Fano varieties with terminal $\mathbb Q$-factorial singularities and Picard number one is at most 125/2 and this bound is sharp. Bibliography: 21 titles. 
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Yu. G. Prokhorov. The degree of $\mathbb Q$-Fano threefolds. Sbornik. Mathematics, Tome 198 (2007) no. 11, pp. 1683-1702. http://geodesic.mathdoc.fr/item/SM_2007_198_11_a6/

[1] Y. Kawamata, “Boundedness of $\mathbf Q$-Fano threefolds”, Proceedings of the International Conference on Algebra. Part 3 (Novosibirsk, 1989), Contemp. Math., 131, Amer. Math. Soc., Providence, RI, 1992, 439–445 | MR | Zbl

[2] Y. Namikawa, “Smoothing Fano 3-folds”, J. Algebraic Geom., 6:2 (1997), 307–324 | MR | Zbl

[3] M. Reid, “Young person's guide to canonical singularities”, Algebraic geometry. Part 1 (Brunswick, Maine, 1985), Proc. Sympos. Pure Math., 46, Amer. Math. Soc., Providence, RI, 1987, 345–414 | MR | Zbl

[4] K. Suzuki, “On Fano indices of $\mathbb Q$-Fano 3-folds”, Manuscripta Math., 114:2 (2004), 229–246 | DOI | MR | Zbl

[5] V. Alexeev, “General elephants of $\mathbb Q$-Fano 3-folds”, Compositio Math., 91:1 (1994), 91–116 | MR | Zbl

[6] H. Takagi, “On classification of $\mathbb Q$-Fano 3-folds of Gorenstein index 2. I, II”, Nagoya Math. J., 167 (2002), 117–155, 157–216 | MR | Zbl

[7] H. Takagi, “Classification of primary $\mathbb Q$-Fano threefolds with anti-canonical Du Val $K3$ surfaces. I”, J. Algebraic Geom., 15:1 (2006), 31–85 | MR | Zbl

[8] Yu. G. Prokhorov, “On the degree of Fano threefolds with canonical Gorenstein singularities”, Sb. Math., 196:1 (2005), 77–114 | DOI | MR | Zbl

[9] Yu. G. Prokhorov, “On Fano–Enriques threefolds”, Sb. Math., 198:4 (2007), 559–574 | DOI | MR

[10] V. A. Iskovskikh, Yu. G. Prokhorov, Fano varieties, Algebraic geometry V, Encyclopaedia Math. Sci., 47, Springer-Verlag, Berlin, 1999 | MR | Zbl

[11] Y. Kawamata, “Crepant blowing-up of 3-dimensional canonical singularities and its application to degenerations of surfaces”, Ann. of Math. (2), 127:1 (1988), 93–163 | DOI | MR | Zbl

[12] J. Kollár, Y. Miyaoka, S. Mori, H. Takagi, “Boundedness of canonical $\mathbf Q$-Fano 3-folds”, Proc. Japan Acad. Ser. A Math. Sci., 76:5 (2000), 73–77 | DOI | MR | Zbl

[13] S. Mori, Yu. G. Prokhorov, “On $\mathbf Q$-conic bundles”, Publ. Res. Inst. Math. Sci. (to appear)

[14] T. Fujita, “On the structure of polarized varieties with $\Delta$-genera zero”, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 22 (1975), 103–115 | MR | Zbl

[15] Sh. Mukai, “New developments in the theory of Fano threefolds: vector bundle method and moduli problems”, Sugaku Expositions, 15:2 (2002), 125–150 | MR

[16] F. Ambro, “Ladders on Fano varieties”, J. Math. Sci. (New York), 94:1 (1999), 1126–1135 | DOI | MR | Zbl

[17] J. Kollár, N. I. Shepherd-Barron, “Threefolds and deformations of surface singularities”, Invent. Math., 91:2 (1988), 299–338 | DOI | MR | Zbl

[18] T. Kawachi, V. Maşek, “Reider-type theorems on normal surfaces”, J. Algebraic Geom., 7:2 (1998), 239–249 | MR | Zbl

[19] I. Reider, “Vector bundles of rank 2 and linear systems on algebraic surfaces”, Ann. of Math. (2), 127:2 (1988), 309–316 | DOI | MR | Zbl

[20] 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

[21] V. V. Shokurov, “3-fold log flips”, Russian Acad. Sci. Izv. Math., 40:1 (1993), 95–202 | DOI | MR | Zbl