Geodesic
Separation properties for closures of toric orbits
Sbornik. Mathematics, Tome 197 (2006) no. 3, pp. 415-432 
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/
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     url = {http://geodesic.mathdoc.fr/item/SM_2006_197_3_a5/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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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[5] Dzh. Khamfri, Lineinye algebraicheskie gruppy, Nauka, M., 1980 | MR

[6] W. Fulton, Introduction to toric varieties, Ann. of Math. Stud., 131, Princeton Univ. Press, Princeton, NJ, 1993 | MR | Zbl

[7] B. Sturmfels, Gröbner bases and convex polytopes, Univ. Lecture Ser., 8, Amer. Math. Soc., Providence, RI, 1996 | MR | Zbl