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Archiv der Mathematik

, Volume 89, Issue 4, pp 315–325 | Cite as

On the moduli of surfaces admitting genus two fibrations over elliptic curves

  • Gülay Karadoğan-Kaya
Article
  • 49 Downloads

Abstract.

In this paper, we study the structure, deformations and the moduli spaces of complex projective surfaces admitting genus two fibrations over elliptic curves. We observe that a surface admitting a smooth fibration as above is elliptic, and we employ results on the moduli of polarized elliptic surfaces to construct moduli spaces of these smooth fibrations. In the case of nonsmooth fibrations, we relate the moduli spaces to the Hurwitz schemes \({\mathcal{H}}(1,X(d), n)\) of morphisms of degree n from elliptic curves to the modular curve X(d), d ≥ 3. Ultimately, we show that the moduli spaces in the nonsmooth case are fiber spaces over the affine line \({\mathbb{A}}^1\) with fibers determined by the components of \({\mathcal{H}}(1,X(d), n)\).

Mathematics Subject Classification (2000).

Primary 14D22 Secondary 14J10 

Keywords.

Moduli spaces fibrations Hurwitz schemes 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2007

Authors and Affiliations

  1. 1.Departement of MathematicsGalatasaray UniversityOrtakoy, IstanbulTurkey

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