Februray 2017, Moscow, Russia

Title: Birational geometry of del Pezzo fibrations

Abstract: Del Pezzo brations appear as minimal models of rationally connected varieties. The rationality of smooth del Pezzo brations is a well studied question but smooth brations are not dense in moduli. Little is known about the rationality of the singular models. We prove
birational rigidity, hence non-rationality, of del Pezzo brations with simple non-Gorenstein singularities satisfying the famous K²-condition. We then apply this result to study embeddings of PSL₂(7) into the Cremona group.