An adjoint variety X (g) associated to a complex simple Lie algebra g is by definition a projective variety in ℙ*(g) obtained as the projectivization of the (unique) non-zero, minimal nilpotent orbit in g. We first describe the tangent loci of X (g) in terms of s-fraktur sign and l-fraktur sign2-triples. Secondly for a graded decomposition of contact type g = ⊕-2≤i≤2gi, we show that the intersection of X (g) and the linear subspace ℙ*(g1) in ℙ*(g) coincides with the cubic Veronese variety associated to g.
|Number of pages||10|
|Journal||Nagoya Mathematical Journal|
|Publication status||Published - 2000 Jun|
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