Birationally Rigid Complete Intersections of Codimension Three

In this work, we study the birational geometry of Fano complete intersections of codimension three. In particular, we establish that they are birational superrigid, given certain regularity conditions. We also provide an estimate for the codimension of the set of such complete intersections with non-regular points. Furthermore, we show, using the 4n^{2}-inequality for complete intersection singularities, and the technique of hypertangent divisors, that in the parameter space of (M+3)-dimensional Fano complete intersections of codimension three, the codimension of the complement to the set of birationally superrigid complete intersections is at least [1/2(M-10)(M-11)]-2 for M not less than 30. We also determine the minimal dimension such that a regular complete intersection V is birationally superrigid given the removal of the last a in {1,2,3,4,5} hypertangent divisors