Preprint A29/2001
Secants, tangents and the homogeneity of Freudenthal varieties of certain type

Osami YASUKURA | KAJI, Hajime

**Keywords: **
Freudenthal varieties | secant loci | tangent loci | homogeneity

For a given simple, graded Lie algebra
g = g_{-2} + ... + g_1 + g_2 of contact type,
we define a certain projective variety V
in the projectivization of g_1
in terms of the Lie bracket, and call V
the Freudenthal variety associated to g.
In this article, we introduce
a certain stratification of the ambient space of V,
and discuss about projective geometry of V,
especially, their secant and tangent loci.
We discuss also about the homogeneity of V.