Sala Seminari (Dip. Matematica).
Kodaira fibrations are surfaces of general type with a non-isotrivial fibration, which are differentiable fibre bundles. First examples were constructed by Kodaira and Atiyah to show that the signature need not be multiplicative in fibre bundles. We review approaches to construct such surfaces with focus on controlling the signature. From this we obtain new examples with signature 16. (Joint work with Ju A Lee and Michael Lönne)