Birationally rigid complete intersections of high codimension

Abstract

Abstract We prove that a Fano complete intersection of codimension and index in the complex projective space for and with at most multi-quadratic singularities is birationally superrigid. The codimension of the complement of the set of birationally superrigid complete intersections in the natural moduli space is shown to be at least . The proof is based on the technique of hypertangent divisors combined with the recently discovered -inequality for complete intersection singularities.