Birationally rigid hypersurfaces with quadratic singularities of low rank

被引：0

作者：

Pukhlikov, A. V. ^{[1
]}

机构：

[1] Univ Liverpool, Dept Math Sci, Liverpool, England

来源：

SBORNIK MATHEMATICS | 2024年 / 215卷 / 06期

关键词：

Fano variety; birational rigidity; quadratic singularity; COMPLETE-INTERSECTIONS; FANO; GEOMETRY;

D O I：

10.4213/sm10061e

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is shown that hypersurfaces of degree M in P-M , M >= 5 , with at most quadratic singularities of rank at least 3 that satisfy certain conditions of general position are birationally superrigid Fano varieties and for M >= 8 the complement to the set of such hypersurfaces is of co dimension at least ((M-1)(2)) + 1 with respect to the natural parameter space. Bibliography: 18 titles.

引用

页码：823 / 840

页数：18

共 18 条

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Evans, D.
Pukhlikov, A., V
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[7] Krylov I., ARXIV
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Krylov, Igor
[J]. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 2018, 97 : 222 - 246
[9] Pukhlikov A., 2017, Arnold Math. J, V3, P187
[10] Pukhlikov A., 2013, Birationally Rigid Varieties, V190

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