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.
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Acknowledgments
The author is grateful to Yurii Prokhorov for numerous useful discussions, to Alexander Kuznetsov, Dmitrii Mineev, and Constantin Shramov for their valuable suggestions, to Jérémy Blanc for posing Question 2.6, and to the referee for comments on Theorem 4.3.
Funding
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.
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Russian Text © The Author(s), 2019, published in Matematicheskie Zametki, 2019, Vol. 106, No. 6, pp. 881–893.
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Loginov, K.V. On Nonrational Fibers of del Pezzo Fibrations over Curves. Math Notes 106, 930–939 (2019). https://doi.org/10.1134/S0001434619110294
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DOI: https://doi.org/10.1134/S0001434619110294