Geodesic
Separation properties for closures of toric orbits
Sbornik. Mathematics, Tome 197 (2006) no. 3, pp. 415-432

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A subset $X$ of a vector space $V$ is said to have the ‘separation property’ if it separates linear forms in the following sense: for each pair $(\alpha,\beta)$ of linearly independent forms on $V$ there exists a point $x\in X$ such that $\alpha(x)=0$ and $\beta(x)\ne0$; equivalently, each homogeneous hyperplane $H\subseteq V$ is linearly spanned by its intersection with $X$. For orbit closures in representation spaces of an algebraic torus a criterion for the separation property is obtained. Strong and weak separation properties are also considered. Bibliography: 7 titles. 
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     author = {O. V. Chuvashova},
     title = {Separation properties for closures of toric orbits},
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     year = {2006},
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O. V. Chuvashova. Separation properties for closures of toric orbits. Sbornik. Mathematics, Tome 197 (2006) no. 3, pp. 415-432. http://geodesic.mathdoc.fr/item/SM_2006_197_3_a5/