Birational rigidity of certain classes of higher-dimensional Fano varieties

点击翻译按钮获取中文摘要

The aim of the project is to study birational geometry of certain classes of higher-dimensional Fano varieties and prove their birational rigidity, including a description of their groups of birational self-maps. The work is based on the techniques of the method of maximal singularities: the Noether-Fano type inequalities, counting multiplicities and inversion of adjunction. It is planned to put a special emphasis on singular varieties that so far were not studied from the viewpoint of their birational (super)rigidity, showing their factoriality and characterising their singularities in order to obtain effective bounds for the co-dimension of the complement to the set of birationally rigid varieties.