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Matematicheskie Zametki, 2001, Volume 69, Issue 4, Pages 550–565
DOI: https://doi.org/10.4213/mzm522 (Mi mzm522) 		 
This article is cited in 12 scientific papers (total in 12 papers)

On Fibrations into del Pezzo Surfaces

M. M. Grinenko

Steklov Mathematical Institute, Russian Academy of Sciences
Full-text PDF (276 kB) Citations (12)
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DOI: https://doi.org/10.4213/mzm522
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).
Received: 08.06.2000
English version:
Mathematical Notes, 2001, Volume 69, Issue 4, Pages 499–513
DOI: https://doi.org/10.1023/A:1010208214029
Bibliographic databases:
Document Type: Article
UDC: 512
Language: Russian
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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    • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математические заметки Mathematical Notes
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