On nonrational fibers of del Pezzo fibrations over curves. (English. Russian original) Zbl 1445.14020
Math. Notes 106, No. 6, 930-939 (2019); translation from Mat. Zametki 106, No. 6, 881-893 (2019).
Summary: 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.
MSC:
| 14D06 | Fibrations, degenerations in algebraic geometry |
| 14J10 | Families, moduli, classification: algebraic theory |
| 14J26 | Rational and ruled surfaces |
| 14J60 | Vector bundles on surfaces and higher-dimensional varieties, and their moduli |
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