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2000 Tangent loci and certain linear sections of adjoint varieties
Hajime Kaji, Osami Yasukura
Nagoya Math. J. 158(none): 63-72 (2000).

Abstract

An adjoint variety $X(\mathfrak{g})$ associated to a complex simple Lie algebra $\mathfrak{g}$ is by definition a projective variety in $\mathbb {P}_{*}(\mathfrak{g})$ obtained as the projectivization of the (unique) non-zero, minimal nilpotent orbit in $\mathfrak{g}$. We first describe the tangent loci of $X(\mathfrak{g})$ in terms of $\mathfrak{sl}_{2}$-triples. Secondly for a graded decomposition of contact type $\mathfrak{g} = \oplus_{-2 \le i \le 2}\, \mathfrak{g}_{i}$, we show that the intersection of $X(\mathfrak{g})$ and the linear subspace $\mathbb {P}_*(\mathfrak{g}_{1})$ in $\mathbb {P}_{*}$$(\mathfrak{g})$ coincides with the cubic Veronese variety associated to $\mathfrak{g}$.

Citation

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Hajime Kaji. Osami Yasukura. "Tangent loci and certain linear sections of adjoint varieties." Nagoya Math. J. 158 63 - 72, 2000.

Information

Published: 2000
First available in Project Euclid: 27 April 2005

zbMATH: 0982.14028
MathSciNet: MR1766575

Subjects:
Primary: 14N05
Secondary: 17B99

Rights: Copyright © 2000 Editorial Board, Nagoya Mathematical Journal

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Vol.158 • 2000
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