utomorphisms of three-dimensional Mori fibrations and Cremona group

In this talk we will classify three-dimensional $G$-del Pezzo varieties of degree $3$ and $4$ which can be $G$-birationally rigid. For some of them we will prove their $G$-birational rigidity. Also we will prove an analogue of the theorem of Sarkisov about existence of a standard model in the case of conic $G$-fibrations.