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).

引用

页数：18

共 39 条

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[32] c1-Cohomological Rigidity for Smooth Toric Fano Varieties of Picard Number Two
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[39] \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$c_1$$\end{document}-Cohomological Rigidity for Smooth Toric Fano Varieties of Picard Number Two
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