January 2016, Charmey, Switzerland

**Title:** Classification and birational rigidity of del Pezzo fibrations with an action of the Klein simple group

**Abstract:** Study of embeddings of a finite group G into the Cremona group is equivalent to study of G-birational geometry of rational G-Mori fiber spaces. A good place to start study finite subgroups is a study of simple subgroup. We prove that any del Pezzo fibration over projective line with an action of the Klein simple group is either a direct product or a certain singular del Pezzo fibration X_{n} of degree 2. It is known that del Pezzo fibrations of degree 2 satisfying the K^{2}-condition are birationally superrigid. I extend this result to singular del Pezzo fibrations and prove that X_{n} are superrigid, in particular not rational, for n>2.