Speaker: Aleksandr Pukhlikov

Title: Birationally rigid higher-dimensional Fano-Mori fibre spaces

Abstract: The first major result on birational rigidity of Fano(-Mori) fibre spaces was the well-known Sarkisov theorem about conic bundles. Since then, the theory gradually progressed to del Pezzo fibrations over the projective line, Fano fibre spaces over the projective line and, recently, to higher-dimensional fibre spaces over higher-dimensional base. In the talk, the earlier results will be reminded and my last theorem on fibre spaces over a higher-dimensional base explained.