Abstract
Let f: X → Y be a dominant morphism from an irreducible, nonsingular algebraic variety X to an algebraic variety Y, such that the field extension f*: k(Y) → k(X) between the rational function fields is separable and k(Y) is algebraically closed in k(X). Then there exists a nonempty open subset V ⊂ Y such that for every y E V the fiber f −1(y) is geometrically integral.
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Bibliographic References
Theorem 7.1, Lemma 7.2, and Corollary 7.3 are presented after [Sha2], and Proposition 7.4 after [Hari].
The concept of a curve of canonical type was introduced by Mumford in [Mum4], from which we took Theorem 7.8, Corollaries 7.9 and 7.10. and Theorems 7.11 and 7.12.
The notion of an exceptional fiber of an elliptic or quasielliptic fibration appeared for the first time in [BM1], from which we took Theorem 7.15 and Corollary 7.17.
Theorem 7.18 is presented after [Mum4] and [3M2].
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© 2001 Springer Science+Business Media New York
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Bădescu, L. (2001). Morphisms from a Surface to a Curve. Elliptic and Quasielliptic Fibrations. In: Algebraic Surfaces. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3512-3_7
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DOI: https://doi.org/10.1007/978-1-4757-3512-3_7
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-3149-8
Online ISBN: 978-1-4757-3512-3
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