Geodesic
Birationally superrigid cyclic triple spaces
Izvestiya. Mathematics , Tome 68 (2004) no. 6, pp. 1229-1275

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We prove the birational superrigidity and non-rationality of a cyclic triple covering of $\mathbb{P}^{2n}$ branched over a nodal hypersurface of degree $3n$ for $n\geqslant 2$. The result obtained solves the problem of birational superrigidity for smooth cyclic triple spaces. We also consider certain relevant problems. 
@article{IM2_2004_68_6_a8,
     author = {I. A. Cheltsov},
     title = {Birationally superrigid cyclic triple spaces},
     journal = {Izvestiya. Mathematics },
     pages = {1229--1275},
     publisher = {mathdoc},
     volume = {68},
     number = {6},
     year = {2004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2004_68_6_a8/}
}
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I. A. Cheltsov. Birationally superrigid cyclic triple spaces. Izvestiya. Mathematics , Tome 68 (2004) no. 6, pp. 1229-1275. http://geodesic.mathdoc.fr/item/IM2_2004_68_6_a8/