Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 63-72 |
| Number of pages | 10 |
| Journal | Nagoya Mathematical Journal |
| Volume | 158 |
| Publication status | Published - 2000 Jun |
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Tangent loci and certain linear sections of adjoint varieties. / Kaji, Hajime; Yasukura, Osami.
In: Nagoya Mathematical Journal, Vol. 158, 06.2000, p. 63-72.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Tangent loci and certain linear sections of adjoint varieties
AU - Kaji, Hajime
AU - Yasukura, Osami
PY - 2000/6
Y1 - 2000/6
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0039622830&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0039622830&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:0039622830
VL - 158
SP - 63
EP - 72
JO - Nagoya Mathematical Journal
JF - Nagoya Mathematical Journal
SN - 0027-7630
ER -