Birationally rigid Fano double hypersurfaces

被引：18
作者：
Pukhlikov, AV [1 ]
机构：
[1] Russian Acad Sci, VA Steklov Math Inst, Moscow 117901, Russia
来源：
SBORNIK MATHEMATICS | 2000年 / 191卷 / 5-6期
关键词：
D O I：
10.1070/SM2000v191n06ABEH000485
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A general Fano double hypersurface V of index 1 (sigma: V --> Q(m) subset of PM+1 is a double cover branched over a smooth divisor W = W-2 iota* subset of PM+1, here m + iota = M + 1 greater than or equal to 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.
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页码：883 / 908
页数：26
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