Journal of Mathematics of Kyoto University

The secant varieties of nilpotent orbits

Yasuhiro Omoda

Full-text: Open access


Let $\mathfrak{g}$ be a complex simple Lie algebra. We have the adjoint representation of the adjoint group $G$ on $\mathfrak{g}$. Then $G$ acts on the projective space $\mathbb{P}_{\mathfrak{g}}$. We consider the closure $X$ of the image of a nilpotent orbit in $\mathbb{P}_{\mathfrak{g}}$. The $i$-secant variety $Sec^{(i)}X$ of a projective variety $X$ is the closure of the union of projective subspaces of dimension $i$ in the ambient space $\mathbb{P}$ spanned by $i+1$ points on $X$. In particular we call the 1-secant variety the secant variety. In this paper we give explicit descriptions of the secant and the higher secant varieties of nilpotent orbits of complex classical simple Lie algebras.

Article information

J. Math. Kyoto Univ. Volume 48, Number 1 (2008), 49-71.

First available in Project Euclid: 14 August 2009

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Omoda, Yasuhiro. The secant varieties of nilpotent orbits. J. Math. Kyoto Univ. 48 (2008), no. 1, 49--71. doi:10.1215/kjm/1250280975.

Export citation