On the moduli of surfaces admitting genus two fibrations over elliptic curves |
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Authors: | Gülay Karadoğan-Kaya |
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Institution: | (1) Departement of Mathematics, Galatasaray University, Ciragan Str. No:36, 34357 Ortakoy, Istanbul, Turkey |
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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
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
with fibers determined by the components of
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Received: 30 August 2006 |
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Keywords: | Primary 14D22 Secondary 14J10 |
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