Abstract
For a reductive Lie algbera over an algbraically closed field of charasteristic zero, we consider a borel subgroup $B$ of its adjoint group, a Cartan subalgebra contained in the Lie algebra of $B$ and the closure $X$ of its orbit under $B$ in the Grassmannian. The variety $X$ plays an important role in the study of the commuting variety. In this note, we prove that $X$ is Gorenstein with rational singularities.
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