Algebraic geometry seminar in New-York University

March, 2016, New-York, USA

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 studying finite subgroups in Cremona group is a study of simple subgroups. I 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 Xn of degree 2. It is known that del Pezzo fibrations of degree 2 satisfying the K2-condition are birationally superrigid. I extend this result to singular del Pezzo fibrations and prove that Xn are superrigid, in particular not rational, for n>2.