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Rigidity of projective symmetric manifolds of Picard number 1 associated to composition algebras
- Source :
- Épijournal de Géométrie Algébrique, Special volume in honour of Claire Voisin (July 20, 2023) epiga:10432
- Publication Year :
- 2022
-
Abstract
- 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 $X(\mathbb{A})$.
- Subjects :
- Mathematics - Algebraic Geometry
Subjects
Details
- Database :
- arXiv
- Journal :
- Épijournal de Géométrie Algébrique, Special volume in honour of Claire Voisin (July 20, 2023) epiga:10432
- Publication Type :
- Report
- Accession number :
- edsarx.2212.02799
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.46298/epiga.2023.10432