Equidimensional actions of algebraic tori

Nakajima, Haruhisa

Annales de l'Institut Fourier, Tome 45 (1995) no. 3, pp. 681-705.

Soit $X$ une variété affine conique factorielle sur un corps algébriquement clos de caractéristique zéro. Nous considérons les actions équidimensionnelles, algébriques, et stables d’un tore algébrique sur $X$ qui sont compatibles avec la structure conique. Nous montrons que de telles actions sont colibres et que les nilcônes de $X$ qui lui sont associés sont des intersections complètes.

Let $X$ be an affine conical factorial variety over an algebraically closed field of characteristic zero. We consider equidimensional and stable algebraic actions of an algebraic torus on $X$ compatible with the conical structure. We show that such actions are cofree and the nullcones of $X$ associated with them are complete intersections.

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