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Sbornik: Mathematics, 2001, Volume 192, Issue 10, Pages 1543–1551
DOI: https://doi.org/10.1070/SM2001v192n10ABEH000605
(Mi sm605)
 

This article is cited in 13 scientific papers (total in 13 papers)

On a series of birationally rigid varieties with a pencil of Fano hypersurfaces

I. V. Sobolev

M. V. Lomonosov Moscow State University
References:
Abstract: We show that a general divisor of bidegree (2,M) in P1×PM for M4 is a birationally rigid variety and that the group of its birational automorphisms consists of two elements.
Received: 10.04.2001
Bibliographic databases:
UDC: 512.6
MSC: Primary 14E07; Secondary 14J45
Language: English
Original paper language: Russian
Citation: I. V. Sobolev, “On a series of birationally rigid varieties with a pencil of Fano hypersurfaces”, Sb. Math., 192:10 (2001), 1543–1551
Citation in format AMSBIB
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\by I.~V.~Sobolev
\paper On a series of birationally rigid varieties with a~pencil of Fano hypersurfaces
\jour Sb. Math.
\yr 2001
\vol 192
\issue 10
\pages 1543--1551
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Linking options:
  • https://www.mathnet.ru/eng/sm605
  • https://doi.org/10.1070/SM2001v192n10ABEH000605
  • https://www.mathnet.ru/eng/sm/v192/i10/p123
  • This publication is cited in the following 13 articles:
    1. Johannes Nicaise, John Christian Ottem, “Tropical degenerations and stable rationality”, Duke Math. J., 171:15 (2022)  crossref
    2. A. V. Pukhlikov, “Birationally rigid Fano fibre spaces. II”, Izv. Math., 79:4 (2015), 809–837  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. 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
    4. A. V. Pukhlikov, “Birationally rigid varieties. II. Fano fibre spaces”, Russian Math. Surveys, 65:6 (2010), 1083–1171  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    5. Aleksandr V. Pukhlikov, Cohomological and Geometric Approaches to Rationality Problems, 2010, 275  crossref
    6. Pukhlikov A.V., “Birational geometry of algebraic varieties with a pencil of Fano cyclic covers”, Pure Appl. Math. Q., 5:2 (2009), 641–700  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
    7. 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
    8. A. V. Pukhlikov, “Birationally rigid varieties with a pencil of Fano double covers. III”, Sb. Math., 197:3 (2006), 335–368  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    9. 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  scopus  scopus
    10. A. V. Pukhlikov, “Birational geometry of Fano direct products”, Izv. Math., 69:6 (2005), 1225–1255  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    11. 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
    12. 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
    13. A. V. Pukhlikov, “Birationally rigid iterated Fano double covers”, Izv. Math., 67:3 (2003), 555–596  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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