Geodesic
Truncation of systems of polynomial equations, ideals and varieties
Izvestiya. Mathematics, Tome 63 (1999) no. 3, pp. 535-547 
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/
@article{IM2_1999_63_3_a3,
     author = {B. Ya. Kazarnovskii},
     title = {Truncation of systems of polynomial equations, ideals and varieties},
     journal = {Izvestiya. Mathematics},
     pages = {535--547},
     year = {1999},
     volume = {63},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1999_63_3_a3/}
}
TY  - JOUR
AU  - B. Ya. Kazarnovskii
TI  - Truncation of systems of polynomial equations, ideals and varieties
JO  - Izvestiya. Mathematics
PY  - 1999
SP  - 535
EP  - 547
VL  - 63
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/IM2_1999_63_3_a3/
LA  - en
ID  - IM2_1999_63_3_a3
ER  - 
%0 Journal Article
%A B. Ya. Kazarnovskii
%T Truncation of systems of polynomial equations, ideals and varieties
%J Izvestiya. Mathematics
%D 1999
%P 535-547
%V 63
%N 3
%U http://geodesic.mathdoc.fr/item/IM2_1999_63_3_a3/
%G en
%F IM2_1999_63_3_a3

Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] Kemph G., Knudsen F., Mamford D., Saint-Donat B., Toroidal embeddings, Lect. Notes Math., 339, Springer-Verlag, 1973 | MR

[2] Danilov V. I., “Geometriya toricheskikh mnogoobrazii”, UMN, 33:2 (1978), 85–134 | MR | Zbl

[3] Arnold V. I., Varchenko A. N., Gusein-Zade S. M., Osobennosti differentsiruemykh otobrazhenii. Monodromiya i osobennosti integralov, Nauka, M., 1994 | MR

[4] Gelfond O. A., Khovanskii A. G., “Mnogogranniki Nyutona i vychety Grotendika”, Dokl. RAN, 3:350 (1996), 298–300 | MR | Zbl

[5] Kazarnovskii B. Ya., “Eksponentsialnye analiticheskie mnozhestva”, Funktsion. analiz i ego prilozh., 31:2 (1997), 15–26 | MR | Zbl

[6] Khovanskii A. G., “Summy konechnykh mnozhestv, orbity kommutativnykh polugrupp i funktsii Gilberta”, Funktsion. analiz i ego prilozh., 29:3 (1995), 36–50 | MR

[7] Atya M., Makdonald I., Vvedenie v kommutativnuyu algebru, Mir, M., 1972 | MR