Resumen de Birational superrigidity is not a locally closed property
We prove an optimal result on the birational rigidity and K-stability of index 1 hypersurfaces in Pn+1 with ordinary singularities when n≫0 and also study the birational superrigidity and K-stability of certain weighted complete intersections. As an application, we show that birational superrigidity is not a locally closed property in moduli. We also prove (in the Appendix) that the alpha invariant function is constructible in some families of complete intersections.
