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Izv. RAN. Ser. Mat., 2015, Volume 79, Issue 4, Pages 175–204 (Mi izv8273)  

This article is cited in 11 scientific papers (total in 11 papers)

Birationally rigid Fano fibre spaces. II

A. V. Pukhlikov

University of Liverpool

Abstract: We prove the birational rigidity of large classes of Fano–Mori fibre spaces over a base of arbitrary dimension bounded above by a constant that depends only on the dimension of the fibres. To do this, we first show that if every fibre of a Fano–Mori fibre space satisfies certain natural conditions, then every birational map onto another such space is fibrewise. Then we construct large classes of fibre spaces (whose fibres are either Fano double spaces of index 1 or Fano hypersurfaces of index 1) satisfying these conditions.

Keywords: Fano–Mori fibre space, birational rigidity, maximal singularity, hypertangent divisor, log canonical singularity, linear system, canonical class.

DOI: https://doi.org/10.4213/im8273

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English version:
Izvestiya: Mathematics, 2015, 79:4, 809–837

Bibliographic databases:

UDC: 512.7
MSC: 14E05, 14J45, 14D06, 14M22, 14E30
Received: 02.07.2014

Citation: A. V. Pukhlikov, “Birationally rigid Fano fibre spaces. II”, Izv. RAN. Ser. Mat., 79:4 (2015), 175–204; Izv. Math., 79:4 (2015), 809–837

Citation in format AMSBIB
\by A.~V.~Pukhlikov
\paper Birationally rigid Fano fibre spaces. II
\jour Izv. RAN. Ser. Mat.
\yr 2015
\vol 79
\issue 4
\pages 175--204
\jour Izv. Math.
\yr 2015
\vol 79
\issue 4
\pages 809--837

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  • https://doi.org/10.4213/im8273
  • http://mi.mathnet.ru/eng/izv/v79/i4/p175

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    This publication is cited in the following articles:
    1. Pukhlikov V A., “Canonical and Log Canonical Thresholds of Multiple Projective Spaces”, Eur. J. Math.  crossref  isi
    2. Kim I.-K. Okada T. Won J., “Alpha Invariants of Birationally Bi-Rigid Fano 3-Folds i”, Eur. J. Math.  crossref  mathscinet  isi
    3. A. V. Pukhlikov, “Birational geometry of algebraic varieties fibred into Fano double spaces”, Izv. Math., 81:3 (2017), 618–644  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    4. E. Johnstone, “Birationally Rigid Singular Double Quadrics and Double Cubics”, Math. Notes, 102:4 (2017), 508–515  mathnet  crossref  crossref  mathscinet  isi  elib
    5. C. Fontanari, D. Martinelli, “A remark on rationally connected varieties and mori dream spaces”, Proc. Edinb. Math. Soc., 62:1 (2019), 259–263  crossref  isi
    6. D. Evans, A. V. Pukhlikov, “Birationally rigid complete intersections of high codimension”, Izv. Math., 83:4 (2019), 743–769  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    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
    8. V A. Pukhlikov, “Birational geometry of singular fano hypersurfaces of index two”, Manuscr. Math., 161:1-2 (2020), 161–203  crossref  isi
    9. V A. Pukhlikov, “Rationally connected rational double covers of primitive fano varieties”, Epijournal Geom. Algebr., 4 (2020), 18  mathscinet  zmath  isi
    10. A. V. Pukhlikov, “Birational geometry of singular Fano double spaces of index two”, Sb. Math., 212:4 (2021), 551–566  mathnet  crossref  crossref  isi
    11. A. V. Pukhlikov, “Remarks on Galois Rational Coverings”, Math. Notes, 110:2 (2021), 242–247  mathnet  crossref  crossref  isi
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