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Matematicheskie Zametki, 2019, Volume 106, Issue 6, Pages 881–893
DOI: https://doi.org/10.4213/mzm12257 (Mi mzm12257) 		 
This article is cited in 2 scientific papers (total in 2 papers)

On Nonrational Fibers of del Pezzo Fibrations over Curves

K. V. Loginov

Laboratory of algebraic geometry and its applications, National Research University "Higher School of Economics" (HSE), Moscow
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DOI: https://doi.org/10.4213/mzm12257
Abstract: We consider threefold del Pezzo fibrations over a curve germ whose central fiber is nonrational. Under the additional assumption that the singularities of the total space are at worst ordinary double points, we apply a suitable base change and show that there is a one-to-one correspondence between such fibrations and certain nonsingular del Pezzo fibrations equipped with a cyclic group action.
Keywords: Mori fibration, del Pezzo surface, rationality.
Funding agency Grant number
Foundation for the Development of Theoretical Physics and Mathematics BASIS
Ministry of Education and Science of the Russian Federation 5-100
Simons Foundation
This work was supported in part supported by the Russian Academic Excellence Project “5-100”, by the Foundation for the Advancement of Theoretical Physics and Mathematics “BASIS”, and by the Simons Foundation.
Received: 20.11.2018
English version:
Mathematical Notes, 2019, Volume 106, Issue 6, Pages 930–939
DOI: https://doi.org/10.1134/S0001434619110294
Bibliographic databases:
Document Type: Article
UDC: 512.7
Language: Russian
Citation: K. V. Loginov, “On Nonrational Fibers of del Pezzo Fibrations over Curves”, Mat. Zametki, 106:6 (2019), 881–893; Math. Notes, 106:6 (2019), 930–939
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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