Geodesic
Truncation of systems of polynomial equations, ideals and varieties
Izvestiya. Mathematics , Tome 63 (1999) no. 3, pp. 535-547.

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The main result of this paper is the construction of special so-called locked polynomial ideals to represent systems of equations, and to enable the behaviour of the corresponding algebraic varieties at infinity to be controlled. A consequence of this result is the existence, modulo the action of tori, of a standard minimal toric compactification of an irreducible two-dimensional variety. 
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B. Ya. Kazarnovskii. Truncation of systems of polynomial equations, ideals and varieties. Izvestiya. Mathematics , Tome 63 (1999) no. 3, pp. 535-547. http://geodesic.mathdoc.fr/item/IM2_1999_63_3_a3/

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