On the moduli of surfaces admitting genus two fibrations over elliptic curves (Q2474109)

This paper studies moduli spaces of complex projective surfaces with irregularity 2 which admit a fibration over an elliptic curve E with general fibre of genus 2. The case of smooth fibrations (equiv. when the surface has Kodaira dimension 1) is completely described by showing that having such a fibration is equivalent to having an elliptic fibration with two double fibres of the form 2E. The case of nonsmooth fibrations (equiv. when the surface has general type) is studied by using the results on this case obtained by \textit{G. Xiao} [Surfaces fibrées en courbes de genre deux. Lecture Notes in Mathematics. 1137. (Berlin) etc.: Springer-Verlag. (1985; Zbl 0579.14028)]