Februray 2017, Moscow, Russia
Title: Rationality of del Pezzo fibrations and the Cremona group
Abstract: I will talk about embeddings of PSL2(7) into the Cremona group of rank 3. Study of embeddings of a finite group G into the Cremona group is equivalent to study of G-equivariant birational geometry of rational GQ-Mori fiber spaces.
Thus to classify embeddings of PSL2(7) one has to classify rational PSL2(7) Q-Mori fiber spaces up to PSL2(7)-equivariant birational equivalence.
I will discuss classification of PSL2(7) Q-del Pezzo fibrations and their birational rigidity, in particular, rationality.