Abstract
It is proved that the components of degenerate fibers of three-dimensional algebraic manifolds fibered into rational surfaces are rational or irrational ruled suriaces. An example is constructed of a three-dimensional algebraic manifold, fibered into rational surfaces, whose degenerate fiber contains an irrational ruled surface which cannot be eliminated by birational transformations that do not alter the common fiber.
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Translated from Matematicheskie Zametki, Vol. 7, No. 2, pp. 191–202, February, 1970.
In conclusion the author expresses his gratitude to his scientific adviser Yu. I Martin for his assistance.
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Martynov, B.V. Degenerate fibers of three-dimensional manifolds fibered into rational surfaces. Mathematical Notes of the Academy of Sciences of the USSR 7, 115–121 (1970). https://doi.org/10.1007/BF01093493
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DOI: https://doi.org/10.1007/BF01093493