Birationally rigid Fano hypersurfaces
Birationally rigid Fano hypersurfaces
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双有理刚性 Fano 超曲面
DOI：
10.1070/im2002v066n06abeh000413
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
A. Pukhlikov
中科院分区：
文献类型：
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作者：
A. Pukhlikov
证明了光滑Fano超曲面V=V_M\subset{\Bbb P}^M$，$M\geq 6$是双有理超刚性的.特别地，它不能被一个非平凡有理映射纤维化为单圆簇，并且每个到相同维数的极小Fano簇上的双有理映射都是一个双正则同构。证明是基于最大奇异性的方法结合Shokurov和Kollar的连通性原则。
We prove that a smooth Fano hypersurface $V=V_M\subset{\Bbb P}^M$, $M\geq 6$, is birationally superrigid. In particular, it cannot be fibered into uniruled varieties by a non-trivial rational map and each birational map onto a minimal Fano variety of the same dimension is a biregular isomorphism. The proof is based on the method of maximal singularities combined with the connectedness principle of Shokurov and Koll\' ar.