Rigidity of projective symmetric manifolds of Picard number 1 associated to composition algebras

被引：0
|
作者：
Chen, Yifei [1 ,2 ,3 ]
Fu, Baohua [3 ,4 ,5 ]
Li, Qifeng [6 ]
机构：
[1] Chinese Acad Sci, AMSS, 55 ZhongGuanCun East Rd, Beijing 100190, Peoples R China
[2] Chinese Acad Sci, HLM, 55 ZhongGuanCun East Rd, Beijing 100190, Peoples R China
[3] Univ Chinese Acad Sci, Sch Math Sci, Beijing, Peoples R China
[4] Chinese Acad Sci, AMSS, HLM, 55 ZhongGuanCun East Rd, Beijing 100190, Peoples R China
[5] Chinese Acad Sci, MCM, 55 ZhongGuanCun East Rd, Beijing 100190, Peoples R China
[6] Shandong Univ, Qifeng Sch Math, Jinan 250100, Peoples R China
来源：
EPIJOURNAL DE GEOMETRIE ALGEBRIQUE | 2023年 / 2023卷
关键词：
symmetric varieties; DEFORMATION RIGIDITY; VARIETIES; GEOMETRY; SPACES;
D O I：
10.46298/epiga.2023.10432
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
To each complex composition algebra A is associated a projective symmetric manifold X(A) of Picard number 1, which is just a smooth hyperplane section of one of the following varieties: Lag(3, 6), Gr(3, 6), S6, E7/P7. In this paper, we prove that these varieties are rigid; namely, for any smooth family of projective manifolds over a connected base, if one fiber is isomorphic to X(A), then every fiber is isomorphic to X(A).
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页数：18
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