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Mat. Sb., 2003, Volume 194, Number 5, Pages 31–60 (Mi msb734)  

This article is cited in 14 scientific papers (total in 14 papers)

Birational properties of pencils of del Pezzo surfaces of degrees 1 and 2. II

M. M. Grinenko

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: It is proved that certain types of fibring on del Pezzo surfaces of degree 2 are birationally rigid.

DOI: https://doi.org/10.4213/sm734

Full text: PDF file (438 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2003, 194:5, 669–695

Bibliographic databases:

UDC: 512.6
MSC: Primary 14E05; Secondary 14C20, 14C21, 14E30, 14J45
Received: 04.06.2002

Citation: M. M. Grinenko, “Birational properties of pencils of del Pezzo surfaces of degrees 1 and 2. II”, Mat. Sb., 194:5 (2003), 31–60; Sb. Math., 194:5 (2003), 669–695

Citation in format AMSBIB
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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. M. M. Grinenko, “Fibrations into del Pezzo surfaces”, Russian Math. Surveys, 61:2 (2006), 255–300  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  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. K. A. Shramov, “On the rationality of non-singular threefolds with a pencil of Del Pezzo surfaces of degree 4”, Sb. Math., 197:1 (2006), 127–137  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    6. 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
    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. 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
    9. 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
    10. Ahmadinezhad H., “On Del Pezzo Fibrations That Are Not Birationally Rigid”, J. Lond. Math. Soc.-Second Ser., 86:Part 1 (2012), 36–62  crossref  mathscinet  zmath  isi
    11. 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
    12. A. V. Pukhlikov, “Birationally rigid Fano fibre spaces. II”, Izv. Math., 79:4 (2015), 809–837  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    13. Ahmadinezhad H., “On pliability of del Pezzo fibrations and Cox rings”, J. Reine Angew. Math., 723 (2017), 101–125  crossref  mathscinet  zmath  isi
    14. Krylov I., “Birational Geometry of Del Pezzo Fibrations With Terminal Quotient Singularities”, J. Lond. Math. Soc.-Second Ser., 97:2 (2018), 222–246  crossref  mathscinet  zmath  isi  scopus
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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