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Mat. Sb., 2004, Volume 195, Number 11, Pages 119–156 (Mi msb861)  

This article is cited in 12 scientific papers (total in 12 papers)

Birationally rigid varieties with a pencil of Fano double covers. II

A. V. Pukhlikov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: The study of the birational geometry of Fano fibrations $\pi\colon V\to\mathbb P^1$ whose fibres are Fano double hypersurfaces of index 1 is continued. Birational rigidity is proved for the majority of families of this type, which do not satisfy the condition of sufficient twistedness over the base (in particular, this means that there exist no other structures of a fibration into rationally connected varieties) and the groups of birational self-maps are computed. The principal components of the method of maximal singularities are considerably improved, chiefly the techniques of counting multiplicities for fibrations $V/\mathbb P^1$ into Fano varieties over the line.

DOI: https://doi.org/10.4213/sm861

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English version:
Sbornik: Mathematics, 2004, 195:11, 1665–1702

Bibliographic databases:

UDC: 513.6
MSC: 14E05, 14J45
Received: 12.01.2004

Citation: A. V. Pukhlikov, “Birationally rigid varieties with a pencil of Fano double covers. II”, Mat. Sb., 195:11 (2004), 119–156; Sb. Math., 195:11 (2004), 1665–1702

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. A. V. Pukhlikov, “Birational geometry of Fano direct products”, Izv. Math., 69:6 (2005), 1225–1255  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. 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
    3. 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
    4. A. V. Pukhlikov, “Explicit examples of birationally rigid Fano varieties”, Mosc. Math. J., 7:3 (2007), 543–560  mathnet  crossref  mathscinet  zmath
    5. 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
    6. A. V. Pukhlikov, “Birational geometry of Fano double covers”, Sb. Math., 199:8 (2008), 1225–1250  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    7. 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, Part 1 (2009), 641–700  crossref  mathscinet  zmath  isi  elib
    8. 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
    9. A. V. Pukhlikov, “On the multiplicity of solutions of a system of algebraic equations”, Proc. Steklov Inst. Math., 276 (2012), 234–249  mathnet  crossref  mathscinet  isi  elib  elib
    10. 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
    11. A. V. Pukhlikov, “Birationally rigid Fano fibre spaces. II”, Izv. Math., 79:4 (2015), 809–837  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    12. Krylov I., “Rationally Connected Non-Fano Type Varieties”, Eur. J. Math., 4:1, 1, SI (2018), 335–355  crossref  mathscinet  zmath  isi  scopus
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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