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On The Moduli of Surfaces Admitting Genus Two Fibrations Over Elliptic Curves

2006/08/19 by Gülay Kaya, Kaya, Gulay
Computer Science · Mathematics · #14D22 #14J10 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.math/0608489

openalex publication_date 2006/08/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \cal 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 A1 with fibers determined by the components of \cal H(1,X(d),n).

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