Geodesic
Fano direct products as rationally connected fibrations
Fundamentalʹnaâ i prikladnaâ matematika, Tome 10 (2004) no. 4, pp. 183-206
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Combining the connectedness principle of Shokurov and Kollár, we develop a new technique of studying birational maps of natural Fano fiber spaces. We prove that the only structures of a rationally connected fibration on direct products of typical Fano varieties are projections onto the factors. In particular, the groups of biregular and birational self-maps of Fano direct products coincide. 
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A. V. Pukhlikov. Fano direct products as rationally connected fibrations. Fundamentalʹnaâ i prikladnaâ matematika, Tome 10 (2004) no. 4, pp. 183-206. http://geodesic.mathdoc.fr/item/FPM_2004_10_4_a11/

[1] Iskovskikh V. A., Manin Yu. I., “Trekhmernye kvartiki i kontrprimery k probleme Lyurota”, Mat. sb., 86:1 (1971), 140–166 | MR | Zbl

[2] Pukhlikov A. V., “Biratsionalnye avtomorfizmy dvoinogo prostranstva i dvoinoi kvadriki”, Izv. AN SSSR. Ser. mat., 52:1 (1988), 229–239 | MR

[3] Sarkisov V. G., “O strukturakh rassloenii na koniki”, Izv. AN SSSR. Ser. mat., 46:2 (1982), 371–408 | MR | Zbl

[4] Corti A., “Singularities of linear systems and 3-fold birational geometry”, Explicit Birational Geometry of Threefolds, London Math. Soc. Lecture Note Series, 281, Cambridge University Press, 2000, 259–312 | MR | Zbl

[5] Fulton W., Intersection Theory, Springer, 1984 | MR | Zbl

[6] Kawamata Y., “A generalization of Kodaira–Ramanujam's vanishing theorem”, Math. Ann., 261 (1982), 43–46 | DOI | MR | Zbl

[7] Kollár J. et al., Flips and Abundance for Algebraic Threefolds, Asterisque, 211, 1993

[8] Pukhlikov A. V., “Birational isomorphisms of four-dimensional quintics”, Invent. Math., 87 (1987), 303–329 | DOI | MR | Zbl

[9] Pukhlikov A. V., “Birational automorphisms of Fano hypersurfaces”, Invent. Math., 134 (1998), 401–426 | DOI | MR | Zbl

[10] Pukhlikov A. V., “Essentials of the method of maximal singularities”, Explicit Birational Geometry of Threefolds, London Math. Soc. Lecture Note Series, 281, Cambridge University Press, 2000, 73–100 | MR | Zbl

[11] Viehweg E., “Vanishing theorems”, J. Reine Angew. Math., 335 (1982), 1–8 | DOI | MR | Zbl