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.

Anexos:

• STHFV.dvi