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This article is cited in 6 scientific papers (total in 6 papers)
Birationally superrigid cyclic triple spaces
I. A. Cheltsov
Steklov Mathematical Institute, Russian Academy of Sciences
Abstract:
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.
DOI:
https://doi.org/10.4213/im516
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English version:
Izvestiya: Mathematics, 2004, 68:6, 1229–1275
Bibliographic databases:
    
UDC:
512.76
MSC: 14E05, 14E08, 14E20, 14G05, 14J45
Received: 11.05.2004
Citation:
I. A. Cheltsov, “Birationally superrigid cyclic triple spaces”, Izv. RAN. Ser. Mat., 68:6 (2004), 169–220; Izv. Math., 68:6 (2004), 1229–1275
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http://mi.mathnet.ru/eng/izv516https://doi.org/10.4213/im516 http://mi.mathnet.ru/eng/izv/v68/i6/p169
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This publication is cited in the following articles:
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I. A. Cheltsov, “Birationally rigid Fano varieties”, Russian Math. Surveys, 60:5 (2005), 875–965
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I. A. Cheltsov, “Local inequalities and birational superrigidity of Fano varieties”, Izv. Math., 70:3 (2006), 605–639
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Odaka Yu., Okada T., “Birational Superrigidity and Slope Stability of Fano Manifolds”, Math. Z., 275:3-4 (2013), 1109–1119
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E. Johnstone, “Birationally Rigid Singular Double Quadrics and Double Cubics”, Math. Notes, 102:4 (2017), 508–515
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Okada T., “Stable Rationality of Cyclic Covers of Projective Spaces”, Proc. Edinb. Math. Soc., 62:3 (2019), 667–682
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A. V. Pukhlikov, “Birationally Rigid Finite Covers of the Projective Space”, Proc. Steklov Inst. Math., 307 (2019), 232–244
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