The Cayley Grassmannian

Laurent Manivel (1)

1 I2M - Institut de Mathématiques de Marseille

We study the projective variety CG parametrizing four dimensional subalgebras of the complex octonions, which we call the Cayley Grass-mannian. We prove that it is a spherical G2-variety with only three orbits that we describe explicitely. Its cohomology ring has a basis of Schubert type classes and we determine the intersection product completely.

Mots clés: octonion; Cayley algebra; Fano manifold; spherical variety; Schubert class

Domaines: Géométrie algébrique [math.AG]

Laurent Manivel. The Cayley Grassmannian. Journal of Algebra, 2018, ⟨10.1016/j.jalgebra.2018.02.010⟩. ⟨hal-01269989⟩