%0 Journal Article
%T The Cayley Grassmannian
%+ Institut de Mathématiques de Marseille (I2M)
%A Manivel, Laurent
%< avec comité de lecture
%@ 0021-8693
%J Journal of Algebra
%I Elsevier
%8 2018-06
%D 2018
%Z 1602.02127
%R 10.1016/j.jalgebra.2018.02.010
%K octonion
%K Cayley algebra
%K Fano manifold
%K spherical variety
%K Schubert class
%Z Mathematics [math]/Algebraic Geometry [math.AG]Journal articles
%X 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.
%G English
%2 https://hal.science/hal-01269989/document
%2 https://hal.science/hal-01269989/file/cayleygrass2.pdf
%L hal-01269989
%U https://hal.science/hal-01269989
%~ CNRS
%~ UNIV-AMU
%~ EC-MARSEILLE
%~ I2M
%~ I2M-2014-