The double Cayley Grassmannian

Laurent Manivel (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

We study the smooth projective symmetric variety of Picard number one that compactifies the exceptional complex Lie group G2, by describing it in terms of vector bundles on the spinor variety of Spin(14). We call it the double Cayley Grassmannian because quite remarkably, it exhibits very similar properties to those of the Cayley Grassmannian (the other symmetric variety of type G2), but doubled in the certain sense. We deduce among other things that all smooth projective symmetric varieties of Picard number one are infinitesimally rigid.

Mots clés: Exceptional Lie group; octonion; spin representation; symmetric variety; Fano manifold; wonderful variety; vector bundle; rigidity; VMRT

Domaines: Géométrie algébrique [math.AG]

Laurent Manivel. The double Cayley Grassmannian. Math. Research Letters, 2021, 28, pp.1765-1792. ⟨hal-02526769⟩