We prove that a generic (in the sense of Zariski topology) Fano complete intersection V of the type (d_1,...,d_k) in P~(M+k), where d_1+...+d_k=M+k, is birationally superrigid if M≥7, M≥k+3 and max{d_i}≥4. In particular, on the variety V there is exactly one structure of a Mori fibre space (or a rationally connected fibre space), the groups of birational and biregular self-maps coincide, Bir V=Aut V, and the variety V is nonrational. This fact covers a considerably larger range of complete intersections than our result of [J. reine angew. Math 541 (2001), 55-79], which required the condition M≥2k+1.
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机译：我们证明了在P〜（M + k）中类型为（d_1，...，d_k）的泛型（从Zariski拓扑意义上）Fano完全交点V，其中d_1 + ... + d_k = M + k，如果M≥7，M≥k+ 3和max {d_i}≥4，则为双刚性。尤其是，在品种V上，正好有一个Mori纤维空间（或合理连接的纤维空间）的结构，双有理和双正则自映射的组重合，Bir V = Aut V，而品种V是非有理的。这个事实比[J.雷恩·安格。 Math 541（2001），55-79]，它要求条件M≥2k+ 1。
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