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
收藏
页码：823 / 840
页数：18
相关论文
共 50 条
  • [31] Birationally rigid Fano complete intersections. II
    Pukhlikov, Aleksandr V.
    JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2014, 688 : 209 - 218
  • [32] Examples of fano varieties of index one that are not birationally rigid
    Castravet, Ana-Maria
    PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2007, 135 (12) : 3783 - 3788
  • [33] Rank-1 codimension one singularities of positive quadratic differential forms
    Guíñez, V
    Gutierrez, C
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2004, 206 (01) : 127 - 155
  • [34] Versal unfoldings for rank-2 singularities of positive quadratic differential forms
    Guíñez V.
    Sáez E.
    Qualitative Theory of Dynamical Systems, 2002, 3 (2) : 285 - 307
  • [35] Quadratic Killing normal Jacobi operator for real hypersurfaces in complex Grassmannians of rank 2
    Lee, Hyunjin
    Woo, Changhwa
    Suh, Young Jin
    JOURNAL OF GEOMETRY AND PHYSICS, 2021, 160
  • [36] Real Hypersurfaces with Quadratic Killing Normal Jacobi Operator in the Real Grassmannians of Rank Two
    Hyunjin Lee
    Young Jin Suh
    Results in Mathematics, 2021, 76
  • [37] Real Hypersurfaces with Quadratic Killing Normal Jacobi Operator in the Real Grassmannians of Rank Two
    Lee, Hyunjin
    Suh, Young Jin
    RESULTS IN MATHEMATICS, 2021, 76 (03)
  • [38] Birationally rigid Pfaffian Fano 3-folds
    Ahmadinezhad, Hamid
    Okada, Takuzo
    ALGEBRAIC GEOMETRY, 2018, 5 (02): : 160 - 199
  • [39] Birationally rigid Fano fibre spaces. II
    Pukhlikov, A. V.
    IZVESTIYA MATHEMATICS, 2015, 79 (04) : 809 - 837
  • [40] Low-rank quadratic semidefinite programming
    Yuan, Ganzhao
    Zhang, Zhenjie
    Ghanem, Bernard
    Hao, Zhifeng
    NEUROCOMPUTING, 2013, 106 : 51 - 60
12345