Geodesic
Inequalities for Hilbert functions and primary decompositions
Algebra i analiz, Tome 19 (2007) no. 6, pp. 143-172.

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

Upper bounds are found for the characteristic function of a homogeneous polynomial ideal $I$; such estimates were previously known only for a radical ideal $I$. An analog of the first Bertini theorem for primary decompositions is formulated and proved. Also, a new representation for primary ideals and modules is introduced and used, which is convenient from an algorithmic point of view.
Keywords: Characteristic function of an ideal, first Bertini theorem, Hilbert functions. 
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A. L. Chistov. Inequalities for Hilbert functions and primary decompositions. Algebra i analiz, Tome 19 (2007) no. 6, pp. 143-172. http://geodesic.mathdoc.fr/item/AA_2007_19_6_a6/

[1] Kertis Ch., Rainer I., Teoriya predstavlenii konechnykh grupp i assotsiativnykh algebr, Nauka, M., 1969 | MR

[2] Nesterenko Yu. V., “Otsenki kharakteristicheskoi funktsii prostogo ideala”, Matem. sb., 123(165):1 (1984), 11–34 | MR | Zbl

[3] Khartskhorn R., Algebraicheskaya geometriya, Mir, M., 1981 | MR | Zbl

[4] Chistov A. L., “Effektivnaya konstruktsiya lokalnykh parametrov neprivodimykh komponent algebraicheskogo mnogoobraziya”, Tr. S.-Peterburg. mat. o-va, 7, 1999, 230–266 | MR

[5] Chistov A. L., “Effektivnaya konstruktsiya lokalnykh parametrov neprivodimykh komponent algebraicheskogo mnogoobraziya v nenulevoi kharakteristike”, Zap. nauchn. sem. POMI, 326, 2005, 248–278 | MR | Zbl

[6] Chardin M., “Une majoration de la fonction de Hilbert et ses conséquences pour l'interpolation algébrique”, Bull. Soc. Math. France, 117 (1989), 305–318 | MR | Zbl

[7] Chistov A. L., A deterministic polynomial–time algorithm for the first Bertini theorem, Preprint of St. Petersburg Math. Soc., , 2004 http://www.MathSoc.spb.ru

[8] Dubé T. W., “A combinatorial proof of the effective nullstellensatz”, J. Symbolic Comput., 15 (1993), 277–296 | DOI | MR | Zbl

[9] Dubé T. W., “The structure of polynomial ideals and Gröbner bases”, SIAM J. Comput., 19 (1990), 750–775 | DOI | MR

[10] Macaulay F. S., “Some properties of enumeration in the theory of modular systems”, Proc. London Math. Soc. (2), 26 (1927), 531–555 | DOI | Zbl

[11] Sombra M., “Bounds for the Hilbert function of polynomial ideals and for the degrees in the Nullstellensatz”, J. Pure Appl. Algebra, 117–118 (1997), 565–599 | DOI | MR | Zbl

[12] Zariski O., “Pencils on an algebraic variety and a new proof of a theorem of Bertini”, Trans. Amer. Math. Soc., 50 (1941), 48–70 | DOI | MR | Zbl