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

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 $\mathrm{Lag}(3,6),\mathrm{Gr}(3,6),{\mathbb{S}}_6,E_7/P_7.$ 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 $X(\mathbb{A})$.

References in corpus (1)

• Rigidity of wonderful group compactifications under Fano deformations

Cited by in corpus (1)

• Deformation rigidity of the double Cayley Grassmannian