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Izv. RAN. Ser. Mat., 2003, Volume 67, Issue 3, Pages 139–182 (Mi izv438)  

This article is cited in 19 scientific papers (total in 19 papers)

Birationally rigid iterated Fano double covers

A. V. Pukhlikov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: 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.

DOI: https://doi.org/10.4213/im438

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English version:
Izvestiya: Mathematics, 2003, 67:3, 555–596

Bibliographic databases:

UDC: 512.6
MSC: 14E05, 14J45
Received: 21.01.2003

Citation: A. V. Pukhlikov, “Birationally rigid iterated Fano double covers”, Izv. RAN. Ser. Mat., 67:3 (2003), 139–182; Izv. Math., 67:3 (2003), 555–596

Citation in format AMSBIB
\by A.~V.~Pukhlikov
\paper Birationally rigid iterated Fano double covers
\jour Izv. RAN. Ser. Mat.
\yr 2003
\vol 67
\issue 3
\pages 139--182
\jour Izv. Math.
\yr 2003
\vol 67
\issue 3
\pages 555--596

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  • https://doi.org/10.4213/im438
  • http://mi.mathnet.ru/eng/izv/v67/i3/p139

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    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. A. V. Pukhlikov, “Birationally rigid varieties with a pencil of double Fano covers. I”, Sb. Math., 195:7 (2004), 1039–1071  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. A. V. Pukhlikov, “Birationally rigid varieties with a pencil of Fano double covers. II”, Sb. Math., 195:11 (2004), 1665–1702  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. I. A. Cheltsov, “Birationally superrigid cyclic triple spaces”, Izv. Math., 68:6 (2004), 1229–1275  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. A. V. Pukhlikov, “Birational geometry of Fano direct products”, Izv. Math., 69:6 (2005), 1225–1255  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    6. I. A. Cheltsov, “Birationally rigid Fano varieties”, Russian Math. Surveys, 60:5 (2005), 875–965  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    7. Pukhlikov A.V., “Birational geometry of algebraic varieties with a pencil of Fano complete intersections”, Manuscripta Math., 121:4 (2006), 491–526  crossref  mathscinet  zmath  isi  elib  scopus
    8. Cheltsov I., “On nodal sextic fivefold”, Math. Nachr., 280:12 (2007), 1344–1353  crossref  mathscinet  zmath  isi  elib  scopus
    9. A. V. Pukhlikov, “Birationally rigid varieties. I. Fano varieties”, Russian Math. Surveys, 62:5 (2007), 857–942  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    10. A. V. Pukhlikov, “On the self-intersection of a movable linear system”, J. Math. Sci., 164:1 (2010), 119–130  mathnet  crossref  mathscinet  elib
    11. A. V. Pukhlikov, “Birational geometry of Fano double covers”, Sb. Math., 199:8 (2008), 1225–1250  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    12. Pukhlikov A.V., “Birational geometry of algebraic varieties with a pencil of Fano cyclic covers”, Pure Appl. Math. Q., 5:2, Special Issue: In honor of Friedrich Hirzebruch, Part 1 (2009), 641–700  crossref  mathscinet  zmath  isi  elib  scopus
    13. A. V. Pukhlikov, “Existence of the Kähler–Einstein Metric on Certain Fano Complete Intersections”, Math. Notes, 88:4 (2010), 552–558  mathnet  crossref  crossref  mathscinet  isi
    14. A. V. Pukhlikov, “Birational geometry of Fano double spaces of index two”, Izv. Math., 74:5 (2010), 925–991  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    15. A. V. Pukhlikov, “Birationally rigid complete intersections of quadrics and cubics”, Izv. Math., 77:4 (2013), 795–845  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    16. 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
    17. Pukhlikov A.V., “Birationally Rigid Fano Complete Intersections. II”, J. Reine Angew. Math., 688 (2014), 209–218  crossref  mathscinet  zmath  isi  scopus
    18. A. V. Pukhlikov, “Birational geometry of higher-dimensional Fano varieties”, Proc. Steklov Inst. Math., 288, suppl. 2 (2015), S1–S150  mathnet  crossref  crossref  isi  elib
    19. Zhuang Z., “Birational Superrigidity Is Not a Locally Closed Property”, Sel. Math.-New Ser., 26:1 (2020), UNSP 11  crossref  isi
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