Elliptic threefolds - Singularities and non-Kodaira fibres -- Andrea Cattaneo (Università di Parma)

Abstract.

Kodaira's classification of the singular fibres in an elliptic surface no
longer applies in the case of elliptic threefolds or higher dimensional
elliptic fibrations. In fact, the classification problem of the singular
fibres for a general elliptic fibration is sill open.

In this talk, we want to study the case of threefolds in detail: after
making some examples of non-Kodaira fibres, we will focus on the link
between the fibration and its Weierstrass model and, using some
singularity theory, we will prove a structure result for non-Kodaira
fibres for a class of elliptic threefolds which is much considered in the
applications.

Finally, we will briefly discuss some aspects concerning this
classification problem in general and how it is possible to extend the
previous results (this is still a work in progress).