We prove birational superrigidity of generic Fano fiber spaces $V/{\mathbbP}^1$, the fibers of which are Fano complete intersections of index 1 anddimension $M$ in ${\mathbb P}^{M+k}$, provided that $M\geq 2k+1$. The proofcombines the traditional quadratic techniques of the method of maximalsingularities with the linear techniques based on the connectedness principleof Shokurov and Koll\' ar. Certain related results are also considered.
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机译：我们证明了通用Fano纤维空间$ V / {\ mathbbP} ^ 1 $的双超刚性，其中纤维是$ {\ mathbb P} ^ {M + k} $中索引1和维度$ M $的Fano完整交集，假设$ M \ geq 2k + 1 $。该证明将最大奇异方法的传统二次技术与基于Shokurov和Koll'ar的连通性原理的线性技术相结合。还考虑了某些相关结果。
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