Geodesic
Birationally rigid Fano fibre spaces. II
Izvestiya. Mathematics , Tome 79 (2015) no. 4, pp. 809-837

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We prove the birational rigidity of large classes of Fano–Mori fibre spaces over a base of arbitrary dimension bounded above by a constant that depends only on the dimension of the fibres. To do this, we first show that if every fibre of a Fano–Mori fibre space satisfies certain natural conditions, then every birational map onto another such space is fibrewise. Then we construct large classes of fibre spaces (whose fibres are either Fano double spaces of index 1 or Fano hypersurfaces of index 1) satisfying these conditions.
Keywords: birational rigidity, maximal singularity, hypertangent divisor, log canonical singularity, linear system, canonical class.
Mots-clés : Fano–Mori fibre space 
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     author = {A. V. Pukhlikov},
     title = {Birationally rigid {Fano} fibre spaces. {II}},
     journal = {Izvestiya. Mathematics },
     pages = {809--837},
     publisher = {mathdoc},
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     number = {4},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2015_79_4_a6/}
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A. V. Pukhlikov. Birationally rigid Fano fibre spaces. II. Izvestiya. Mathematics , Tome 79 (2015) no. 4, pp. 809-837. http://geodesic.mathdoc.fr/item/IM2_2015_79_4_a6/