### 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 sign_{2}-triples. Secondly for a graded decomposition of contact type g = ⊕_{-2≤i≤2}g_{i}, we show that the intersection of X (g) and the linear subspace ℙ*(g_{1}) in ℙ*(g) coincides with the cubic Veronese variety associated to g.

Original language | English |
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Pages (from-to) | 63-72 |

Number of pages | 10 |

Journal | Nagoya Mathematical Journal |

Volume | 158 |

Publication status | Published - 2000 Jun |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Nagoya Mathematical Journal*,

*158*, 63-72.

**Tangent loci and certain linear sections of adjoint varieties.** / Kaji, Hajime; Yasukura, Osami.

Research output: Contribution to journal › Article

*Nagoya Mathematical Journal*, vol. 158, pp. 63-72.

}

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 -