We examine the finite group actions on K3 and Abelian surfaces giving the same orbit space after desingularization. We show that when the group is not Z_2, then the Picard number of the K3 surface must be 19 or 20, and that in the latter case the Abelian surface is uniquely determined by the K3 surface.
We consider the arithmetic exceptionality problem for the generalized Lattès maps on $\mathbf{P}^2$. We prove an existence result for maps arising from the product $E \times E$ of elliptic curves $E$ with CM.
In this paper, we investigate the moduli of surfaces of general type admitting genus 2 fibrations with irregularity q = g_b + 1, where g_b >= 2 is the genus of the base. We prove that smooth fibrations are parametrized by a unique component in the moduli space. The same result applies to nonsmooth fibrations with special values of g_b. In the general case, we give a bound on the dimension of the corresponding connected components.
In this note, we show that for surfaces admitting suitable fibrations, any given degeneration X / Delta is bimeromorphic to a fiber space over Delta and we apply this result to the study of the degenerate fiber.
We investigate the relation between the ordinarity of a surface and of its Picard scheme in connection with the problem of lifting fibrations of genus g > 1 on surfaces to characteristic zero.
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