Generalized Shioda-Inose Structures on K3 Surfaces

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.Comment: LaTeX 2.09, 5 pages, To appear in Manuscripta Mat

ON THE STRUCTURE OF GENERALIZED ALBANESE VARIETIES

Given a smooth projective surface X over an algebraically closed field k and a modulus (an effective divisor) m on X, one defines the idle class group Cm(X) of X with modulus m (see 1, chapter III, section 4). The corresponding generalized Albanese variety Gum and the generalized Albanese map um:X|m|Gum have the following universal mapping property (2): if :XG is a rational map into a commutative algebraic group which induces a homomorphism Cm(X)G(k) (1, chapter III, proposition 1), then factors uniquely through um

On the moduli spaces of fiber bundles of curves of genus >= 2

We determine the moduli spaces parametrizing analytic fiber bundles of curves of genus g greater than or equal to 2 over curves of genus g(b) > (g + 1)/2

On symplectic quotients of K3 surfaces

In this note, we construct generalized Shioda-Inose structures on K3 surfaces using cyclic covers and almost functoriality of Shioda-Inose structures with respect to normal subgroups of a given group of symplectic automorphisms

On degenerations of fiber spaces of curves of genus >=2

In this note, we show that for surfaces admitting suitable fibralions, any given degeneration X/Delta is bimeromorphic to a fiber space over a curve Y/Delta and we apply this result to the study of the degenerate fiber

On the moduli of surfaces admitting genus 2 fibrations

We investigate the structure of the components of the moduli space Of Surfaces of general type, which parametrize surfaces admitting nonsmooth genus 2 fibrations of nonalbanese type, over curves of genus g(b) greater than or equal to 2

Generalized Shioda-Inose structures on K3 surfaces

In this note, we study the action of finite groups of symplectic automorphisms on K3 surfaces which yield quotients birational to generalized Kummer surfaces. For each possible group, we determine the Picard number of the K3 surface admitting such an action and for singular K3 surfaces we show the uniqueness of the associated abelian surface