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Mat. Zametki, 2001, Volume 69, Issue 4, Pages 550–565 (Mi mz522)  

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

On Fibrations into del Pezzo Surfaces

M. M. Grinenko

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: The problem of birational rigidity for three-dimensional algebraic varieties fibered over rational curves into del Pezzo surfaces of degree 1 is discussed. A criterion for the rigidity of such fibrations in the Mori category is suggested and the inverse implication is proved (Theorem 3.3). Surgeries on fibers in fibrations of this type, which turn out to be closely related to the rigidity problem, are considered. In particular, an important result on the uniqueness of a smooth model in a class of maps over a base is stated (Corollary 4.5).

DOI: https://doi.org/10.4213/mzm522

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English version:
Mathematical Notes, 2001, 69:4, 499–513

Bibliographic databases:

UDC: 512
Received: 08.06.2000

Citation: M. M. Grinenko, “On Fibrations into del Pezzo Surfaces”, Mat. Zametki, 69:4 (2001), 550–565; Math. Notes, 69:4 (2001), 499–513

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. 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
    2. 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
    3. 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
    4. 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
    5. Cheltsov, I, “Birationally rigid del Pezzo fibrations”, Manuscripta Mathematica, 116:4 (2005), 385  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    6. I. A. Cheltsov, “Local inequalities and birational superrigidity of Fano varieties”, Izv. Math., 70:3 (2006), 605–639  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    7. 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
    8. Bashmakova M.G., “Dva podkhoda k otsenke mery irratsionalnosti znachenii gipergeometricheskoi funktsii s polutselymi parametrami”, Vestnik Bryanskogo gosudarstvennogo tekhnicheskogo universiteta, 2011, no. 2, 114–120  elib
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