Singularities of algebraic subvarieties and problems of birational geometry
The paper under review gives an account on how a method of estimating multiplicities of singularities on an algebraic variety can be applied to the problem of describing birational maps of rationally connected varieties. A variety is \textit{rationally connected} if any two general points on it can be joined by a rational curve. A method of hypertangent divisors is surveyed and it is demonstrated how to construct these divisors on complete intersections. Finally, it is shown how this implies, for instance, that generic hypersurfaces of degree \(d\) in the projective \(d\)-space are birationally superrigid.
scientific article; zbMATH DE number 5809085