Morphisms from a Surface to a Curve. Elliptic and Quasielliptic Fibrations

  • Lucian Bădescu
Part of the Universitext book series (UTX)

Abstract

Let f: XY 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.

Keywords

Exact Sequence Effective Divisor Irreducible Curve Invertible Sheaf Smooth Morphism 
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Bibliographic References

  1. Theorem 7.1, Lemma 7.2, and Corollary 7.3 are presented after [Sha2], and Proposition 7.4 after [Hari].Google Scholar
  2. 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.Google Scholar
  3. 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.Google Scholar
  4. Theorem 7.18 is presented after [Mum4] and [3M2].Google Scholar

Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Lucian Bădescu
    • 1
  1. 1.Institute of MathematicsRomanian AcademyBucharestRomania

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