Deformation rigidity of the double Cayley Grassmannian

Abstract

The double Cayley Grassmannian is a unique smooth equivariant completion with Picard number one of the 14-dimensional exceptional complex Lie group $G_2$, and it parametrizes eight-dimensional isotropic subalgebras of the complexified bi-octonions. We show the rigidity of the double Cayley Grassmannian under Kähler deformations. This means that for any smooth projective family of complex manifolds over a connected base of which one fiber is biholomorphic to the double Cayley Grassmannian, all other fibers are biholomorphic to the double Cayley Grassmannian.

arXiv comment10 pages, 2 figures. arXiv admin note: text overlap with arXiv:1905.06490

References in corpus (4)

• On the deformation rigidity of smooth projective symmetric varieties with Picard number one
• The double Cayley Grassmannian
• Kähler-Einstein metrics on smooth Fano symmetric varieties with Picard number one
• Rigidity of projective symmetric manifolds of Picard number 1 associated to composition algebras