Abstract
It is proved that a general Fano hypersurface of index 1 with isolated singularities in general position is birationally rigid. Hence it cannot be fibred into uniruled varieties of smaller dimension by a rational map, and each -Fano variety with Picard number 1 birationally equivalent to is in fact isomorphic to . In particular, is non-rational. The group of birational self-maps of is either 1 or , depending on whether has a terminal point of the maximum possible multiplicity . The proof is based on a combination of the method of maximal singularities and the techniques of hypertangent systems with Shokurov's connectedness principle.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
