Yifei Chen ; Baohua Fu ; Qifeng Li - Rigidity of projective symmetric manifolds of Picard number 1 associated to composition algebras

epiga:10432 - Épijournal de Géométrie Algébrique, July 20, 2023, Special volume in honour of Claire Voisin - https://doi.org/10.46298/epiga.2023.10432
Rigidity of projective symmetric manifolds of Picard number 1 associated to composition algebras

Authors: Yifei Chen ; Baohua Fu ; Qifeng Li

    To each complex composition algebra $\mathbb{A}$, there associates a projective symmetric manifold $X(\mathbb{A})$ of Picard number one, which is just a smooth hyperplane section of the following varieties ${\rm Lag}(3,6), {\rm Gr}(3,6), \mathbb{S}_6, E_7/P_7.$ In this paper, it is proven that these varieties are rigid, namely for any smooth family of projective manifolds over a connected base, if one fiber is isomorphic to $X(\mathbb{A})$, then every fiber is isomorphic to $X(\mathbb{A})$.


    Volume: Special volume in honour of Claire Voisin
    Published on: July 20, 2023
    Accepted on: July 20, 2023
    Submitted on: December 7, 2022
    Keywords: Mathematics - Algebraic Geometry

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