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Mat. Sb., 2006, Volume 197, Number 3, Pages 35–68 (Mi msb1234)  

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

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

A. V. Pukhlikov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: The study of the birational geometry of Fano fibre spaces $\pi\colon V\to\mathbb P^1$ with fibre that is a Fano double hypersurface of index 1 is completed. For each family of these varieties either the birational rigidity is proved or non-trivial structures of Fano fibre spaces are explicitly produced. A new linear method of the study of movable systems on Fano fibre spaces $V/\mathbb P^1$ is developed.
Bibliography: 17 titles.

DOI: https://doi.org/10.4213/sm1234

Full text: PDF file (668 kB)
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English version:
Sbornik: Mathematics, 2006, 197:3, 335–368

Bibliographic databases:

UDC: 513.6
MSC: 14E05, 14J45
Received: 26.09.2005

Citation: A. V. Pukhlikov, “Birationally rigid varieties with a pencil of Fano double covers. III”, Mat. Sb., 197:3 (2006), 35–68; Sb. Math., 197:3 (2006), 335–368

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. 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
    2. 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
    3. A. V. Pukhlikov, “Birational geometry of Fano double covers”, Sb. Math., 199:8 (2008), 1225–1250  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    4. 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
    5. 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
    6. 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
    7. A. V. Pukhlikov, “Birationally rigid Fano fibre spaces. II”, Izv. Math., 79:4 (2015), 809–837  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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