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This article is cited in 29 scientific papers (total in 29 papers)
Birationally rigid Fano double hypersurfaces
A. V. Pukhlikov Steklov Mathematical Institute, Russian Academy of Sciences
Abstract:
A general Fano double hypersurface $V$ of index 1 $(\sigma\colon V\to Q_m\subset \mathbb P^{M+1}$ is a double cover branched over a smooth divisor $W=W^*_{2l}\subset\mathbb P^{M+1}$, here $m+l=M+1\geqslant 5)$ is proved to be birationally superrigid; in particular, such a hypersurface admits no non-trivial structures of a fibration into uniruled varieties, and it is non-rational. Its groups of birational and biregular automorphisms coincide.
Received: 28.06.1999
Citation:
A. V. Pukhlikov, “Birationally rigid Fano double hypersurfaces”, Sb. Math., 191:6 (2000), 883–908
Linking options:
https://www.mathnet.ru/eng/sm485https://doi.org/10.1070/sm2000v191n06ABEH000485 https://www.mathnet.ru/eng/sm/v191/i6/p101
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Abstract page: | 446 | Russian version PDF: | 177 | English version PDF: | 21 | References: | 95 | First page: | 2 |
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