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Mat. Sb., 2004, Volume 195, Number 7, Pages 127–160 (Mi msb837)  

This article is cited in 8 scientific papers (total in 8 papers)

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

A. V. Pukhlikov

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: The general Fano fibration $\pi\colon V\to\mathbb P^1$ the fibre of which is a double Fano hypersurface of index 1 is proved to be birationally superrigid, provided it is sufficiently twisted over the base. In particular, there exist on $V$ no other structures of a rationally convex fibration. The proof is based on the method of maximal singularities.

DOI: https://doi.org/10.4213/sm837

Full text: PDF file (427 kB)
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English version:
Sbornik: Mathematics, 2004, 195:7, 1039–1071

Bibliographic databases:

Document Type: Article
UDC: 513.6
MSC: 14E05, 14J45
Received: 07.10.2003

Citation: A. V. Pukhlikov, “Birationally rigid varieties with a pencil of double Fano covers. I”, Mat. Sb., 195:7 (2004), 127–160; Sb. Math., 195:7 (2004), 1039–1071

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    This publication is cited in the following articles:
    1. 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
    2. A. V. Pukhlikov, “Birational geometry of Fano direct products”, Izv. Math., 69:6 (2005), 1225–1255  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, “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
    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 Hirzebruch. Part 1 (2009), 641–700  crossref  mathscinet  zmath  isi  elib
    8. 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 - 1992–2005 Sbornik: Mathematics (from 1967)
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