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Mat. Sb., 2000, Volume 191, Number 5, Pages 17–38 (Mi msb475)  

This article is cited in 32 scientific papers (total in 32 papers)

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

M. M. Grinenko

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: The problem of birational rigidity is investigated for smooth Mori fibre spaces representable as a pencil of del Pezzo surfaces of degree 1 or 2.

DOI: https://doi.org/10.4213/sm475

Full text: PDF file (333 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2000, 191:5, 633–653

Bibliographic databases:

Document Type: Article
UDC: 512.6
MSC: Primary 14E05; Secondary 14J45, 14E30, 14C20, 14C21
Received: 27.05.1999

Citation: M. M. Grinenko, “Birational properties of pencils of del Pezzo surfaces of degrees 1 and 2”, Mat. Sb., 191:5 (2000), 17–38; Sb. Math., 191:5 (2000), 633–653

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. V. Pukhlikov, “Fiber-wise birational correspondences”, Math. Notes, 68:1 (2000), 103–112  mathnet  crossref  mathscinet  zmath  isi  elib
    2. M. M. Grinenko, “On Fibrations into del Pezzo Surfaces”, Math. Notes, 69:4 (2001), 499–513  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. M. M. Grinenko, “On fibrewise modifications of fibrings into del Pezzo surfaces of degree 2”, Russian Math. Surveys, 56:4 (2001), 753–754  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    4. I. V. Sobolev, “On a series of birationally rigid varieties with a pencil of Fano hypersurfaces”, Sb. Math., 192:10 (2001), 1543–1551  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    5. I. V. Sobolev, “Birational automorphisms of a class of varieties fibred into cubic surfaces”, Izv. Math., 66:1 (2002), 201–222  mathnet  crossref  crossref  mathscinet  zmath  elib
    6. M. M. Grinenko, “On a double cone over a Veronese surface”, Izv. Math., 67:3 (2003), 421–438  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    7. A. V. Pukhlikov, “Birationally rigid iterated Fano double covers”, Izv. Math., 67:3 (2003), 555–596  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    8. M. M. Grinenko, “Birational properties of pencils of del Pezzo surfaces of degrees 1 and 2. II”, Sb. Math., 194:5 (2003), 669–695  mathnet  crossref  crossref  mathscinet  zmath  isi
    9. Nakashima T., “Stable rank two bundles on Del-Pezzo fibrations of degree 1 or 2”, Arch. Math. (Basel), 81:3 (2003), 258–265  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    10. I. A. Cheltsov, “Birationally superrigid cyclic triple spaces”, Izv. Math., 68:6 (2004), 1229–1275  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    11. M. M. Grinenko, “Mori Structures on a Fano Threefold of Index 2 and Degree 1”, Proc. Steklov Inst. Math., 246 (2004), 103–128  mathnet  mathscinet  zmath
    12. 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
    13. 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
    14. I. A. Cheltsov, “Double space with double line”, Sb. Math., 195:10 (2004), 1503–1544  mathnet  crossref  crossref  mathscinet  zmath  isi
    15. Corti A., Mella M., “Birational geometry of terminal quartic 3-folds. I”, Amer. J. Math., 126:4 (2004), 739–761  crossref  mathscinet  zmath  isi
    16. Cheltsov I., “Birationally rigid del Pezzo fibrations”, Manuscripta Math., 116:4 (2005), 385–396  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    17. V. V. Przyjalkowski, I. A. Cheltsov, K. A. Shramov, “Hyperelliptic and trigonal Fano threefolds”, Izv. Math., 69:2 (2005), 365–421  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    18. A. V. Pukhlikov, “Birational geometry of Fano direct products”, Izv. Math., 69:6 (2005), 1225–1255  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    19. 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
    20. 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
    21. 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
    22. 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
    23. 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
    24. 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  scopus
    25. 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
    26. Vyacheslav V. Shokurov, Sung Rak Choi, “Geography of log models: theory and applications”, centr.eur.j.math, 2011  crossref  mathscinet  isi  scopus  scopus  scopus
    27. 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  scopus  scopus  scopus
    28. 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
    29. A. V. Pukhlikov, “Birationally rigid Fano fibre spaces. II”, Izv. Math., 79:4 (2015), 809–837  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    30. Ahmadinezhad H., “On pliability of del Pezzo fibrations and Cox rings”, J. Reine Angew. Math., 723 (2017), 101–125  crossref  mathscinet  zmath  isi
    31. 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
    32. Yu. G. Prokhorov, “The rationality problem for conic bundles”, Russian Math. Surveys, 73:3 (2018), 375–456  mathnet  crossref  crossref  adsnasa  isi  elib
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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