Birational rigidity of certain classes of higher-dimensional Fano varieties

该项目的目的是研究某些类别的高维Fano簇的双有理几何，并证明它们的双有理刚性，包括描述它们的双有理自映射群。这项工作是基于最大奇异性方法的技术：Noether-Fano型不等式，计数重数和逆的附加。计划把一个特别强调奇异品种，到目前为止还没有研究从他们的双理性（超）刚性的观点，显示他们的factoriality和他们的奇异性的特点，以获得有效的界限的余维的补充集的双理性刚性品种。

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.