Erratum to: Birationally rigid hypersurfaces
Erratum to: Birationally rigid hypersurfaces
复制标题
勘误：双理性刚性超曲面
DOI：
10.1007/s00222-015-0618-4
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发表时间：
2015
影响因子：
3.1
通讯作者：
T. Fernex
中科院分区：
文献类型：
--
作者：
T. Fernex
本文指出了在Invent.Math.192（2013），533 - 566中发表的文章"Birationalitical rigid hypersurfaces"的主要定理证明中的一个空白，并提供了该定理的新证明。原文中引理9.1和引理9.2的陈述是不正确的（有关错误的进一步评论，请参见本说明末尾的备注）。这两个引理被用于证明定理A，这是原文章的主要定理;更准确地说，它们被用于证明定理7.4，定理A是从定理7.4导出的。引理9.2中的错误是由亚诺什·科勒引起我们注意的。虽然引理9.2对于证明不是必不可少的，并且可以被绕过，但是引理9.1中的错误所留下的差距似乎更大，因为引理9.1在定理A的证明中在定理B的应用中起着关键作用。本文对定理A给出了一个新的证明，它不使用定理B，但这并不固定定理7.4的证明，定理7.4应
This note points out a gap in the proof of the main theorem of the article “Birationally rigid hypersurfaces” published in Invent.Math.192 (2013), 533– 566, and provides a new proof of the theorem. The statements of Lemma 9.1 and Lemma 9.2 in the original article are incorrect (see the remarks at the end of this note for further comments on the errors). The two lemmas are used in the proof of Theorem A, which is the main theorem of the original article; more precisely, they are used in the proof of Theorem 7.4 from which Theorem A is deduced. The error in Lemma 9.2 was brought to our attention by Janos Kollar. While Lemma 9.2 is not essential for the proof and can be circumvented, the gap left by the error in Lemma 9.1 appears to be more substantial because of the key role that Lemma 9.1 plays in the application of Theorem B in the proof of Theorem A. In this note, we give a new argument to prove TheoremAwhich does not use TheoremB.This does not fix, however, the proof of Theorem7.4,which should