Birational Superrigidity of Fano Complete Intersections via the Method of Maximal Singularities

Mathematical Applications of Science Fiction We present a transfinite extension of the method ofmaximal singularities to establish the birational super-rigidity of generic Fano complete intersections V ⊂ PNof index 1 and dimension M ≥ 5. By constructing arefined filtration of the group of birational automor-phisms Bir(V ) and utilizing the technique of hyper-tangent distributions, we prove that any birationalmap from V to a Mori fiber space is an isomorphism.Consequently, V admits no non-trivial structure ofa fiber space over a base of positive dimension, andBir(V ) = Aut(V ). We further analyze the stability ofthe log canonical threshold under transfinite perturba-tions of the linear system, providing a rigorous boundon the multiplicity of maximal singularities centeredat subvarieties of codimension ≥ 2.