Geodesic
Birationally rigid iterated Fano double covers
Izvestiya. Mathematics , Tome 67 (2003) no. 3, pp. 555-596

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Iterating the procedure of making a double cover over a given variety, we construct large families of smooth higher-dimensional Fano varieties of index 1. These varieties can be realized as complete intersections in various weighted projective spaces. We prove that a generic variety of these families is birationally superrigid. In particular, it admits no non-trivial structure of a fibration into rationally connected (or even uniruled) varieties, it is non-rational, and its groups of birational and biregular self-maps coincide. 
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     author = {A. V. Pukhlikov},
     title = {Birationally rigid iterated {Fano} double covers},
     journal = {Izvestiya. Mathematics },
     pages = {555--596},
     publisher = {mathdoc},
     volume = {67},
     number = {3},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2003_67_3_a6/}
}
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A. V. Pukhlikov. Birationally rigid iterated Fano double covers. Izvestiya. Mathematics , Tome 67 (2003) no. 3, pp. 555-596. http://geodesic.mathdoc.fr/item/IM2_2003_67_3_a6/