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


Karadogan-Kaya G.

ARCHIV DER MATHEMATIK, vol.89, no.4, pp.315-325, 2007 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 89 Issue: 4
  • Publication Date: 2007
  • Doi Number: 10.1007/s00013-007-2139-x
  • Title of Journal : ARCHIV DER MATHEMATIK
  • Page Numbers: pp.315-325

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 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 a. ne line A(1) with fibers determined by the components of H(1, X(d), n).