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Izv. RAN. Ser. Mat., 2004, Volume 68, Issue 6, Pages 169–220 (Mi izv516)  

This article is cited in 7 scientific papers (total in 7 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

Full text: PDF file (5461 kB)
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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

Citation in format AMSBIB
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\vol 68
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Foord D., “Birationally Rigid Fano Cyclic Covers Over a Hypersurface Containing a Singular Point”, Eur. J. Math.  crossref  isi
    2. I. A. Cheltsov, “Birationally rigid Fano varieties”, Russian Math. Surveys, 60:5 (2005), 875–965  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. I. A. Cheltsov, “Local inequalities and birational superrigidity of Fano varieties”, Izv. Math., 70:3 (2006), 605–639  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    4. Odaka Yu., Okada T., “Birational Superrigidity and Slope Stability of Fano Manifolds”, Math. Z., 275:3-4 (2013), 1109–1119  crossref  mathscinet  zmath  isi  scopus
    5. E. Johnstone, “Birationally Rigid Singular Double Quadrics and Double Cubics”, Math. Notes, 102:4 (2017), 508–515  mathnet  crossref  crossref  mathscinet  isi  elib
    6. Okada T., “Stable Rationality of Cyclic Covers of Projective Spaces”, Proc. Edinb. Math. Soc., 62:3 (2019), 667–682  crossref  isi
    7. A. V. Pukhlikov, “Birationally Rigid Finite Covers of the Projective Space”, Proc. Steklov Inst. Math., 307 (2019), 232–244  mathnet  crossref  crossref  mathscinet  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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