Monodromy of Jacobian Elliptic K3-Surfaces (Michaël Lönne)

A Jacobian elliptic K3 surface S for the talk is a complex projective surface with a fibration map f to the projective line and a section to f called the 0-section.

All regular fibres are elliptic curves, the finitely many singular fibres map to the finite discriminant subset D of the base.

Kodaira investigated the relation between the functional invariant j defined by the j-invariant of fibres, the geometry of singular fibres and the homological invariant which is the monodromy of the topological torus bundle given by the complement in S of the singular fibres.

We consider surfaces with certain geometrical types of singular fibres only and get a classification of monodromy groups in that case.

We end with a discussion of the geometry of the corresponding moduli spaces.

(This talk is based on joint work with Klaus Hulek)