The primitive ideal and Macaulay's inverse system
Sbornik. Mathematics, Tome 191 (2000) no. 7, pp. 945-954 Cet article a éte moissonné depuis la source Math-Net.Ru

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Using the construction of the primitive ideal we describe symbolic powers of a homogeneous radical ideal in a polynomial ring without applying localization. We compute Macaulay's inverse system for the primitive ideal. We consider some applications in the theory of deformations of zero-dimensional singularities and Artinian algebras.
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A. G. Aleksandrov. The primitive ideal and Macaulay's inverse system. Sbornik. Mathematics, Tome 191 (2000) no. 7, pp. 945-954. http://geodesic.mathdoc.fr/item/SM_2000_191_7_a0/

[1] Seibt P., “Differential filtrations and symbolic powers of regular primes”, Math. Z., 166:2 (1979), 146–150 | DOI | MR

[2] Seibt P., “Infinitesimal extensions of commutative algebras”, J. Pure Appl. Algebra, 16:2 (1980), 197–206 | DOI | MR | Zbl

[3] Pellikaan R., “Finite determinacy of functions with non-isolated singularities”, Proc. London Math. Soc. (3), 57 (1988), 357–382 | DOI | MR | Zbl

[4] Aleksandrov A. G., “Duality, derivations and deformations of zero-dimensional singularities”, Zero-dimensional schemes, eds. F. Orecchia, L. Chiantini, Walter de Gruyter, Berlin, 1994, 11–31 | MR

[5] Aleksandrov A. G., “Derivations and deformations of zero-dimensional rings and algebras”, Zero-dimensional commutative rings, eds. D. Anderson, D. Dobbs, Marcel Dekker, Inc., New York, 1995, 81–93 | MR | Zbl

[6] Matsumura H., Commutative algebra, Benjamin, New York, 1970 | MR | Zbl

[7] Zariski O., Samuel P., Commutative algebra, V. 1, Springer-Verlag, New York, 1975 | Zbl

[8] Lichtenbaum S., Schlessinger M., “The cotangent complex of a morphism”, Trans. Amer. Math. Soc., 128:1 (1967), 41–70 | DOI | MR | Zbl

[9] Kleiman S. L., Landolfi J., “Geometry and deformations of special Schubert varieties”, Algebraic geometry, Proc. 5th Nordic Summer-School Math. (Oslo 1970), Wolters-Noordhoff Publ., Groningen, 1972, 97–124 | MR

[10] Ferrand D., “Suite régulière et intersection complète”, C. R. Acad. Sci. Paris. Sér. I Math., 264 (1967), 427–428 | MR | Zbl

[11] Eisenbud D., Hochster A., “Nullstellensatz with nilpotents and Zariski's main lemma on holomorphic functions”, J. Algebra, 58:1 (1979), 137–141 | DOI | MR

[12] Emsalem J., Iarrobino A., “Inverse system of a symbolic power, I”, J. Algebra, 174:3 (1995), 1080–1090 | DOI | MR | Zbl

[13] Ionescu C., “Symbolic powers of prime ideals in polynomial rings”, Kommutative Algebra und Algebraische Geometrie, Tagungsbericht 22/1992, Mathematisches Forschungsinstitut Oberwolfach, Germany, 1992, 9

[14] Macaulay F. H. S., The algebraic theory of modular systems, Cambridge Univ. Press, London, 1916 | MR | Zbl

[15] Mourrain B., “Isolated points, duality and residues”, J. Pure Appl. Algebra, 1997, no. 117–118, 469–493 | DOI | MR | Zbl

[16] Rim D. S., “Formal deformation theory”, Sem. Geom. algebrique Bois-Marie, 1967–1969, SGA 7 I, Lecture Notes in Math., 288, no. 6, 1972, 32–132 | MR | Zbl

[17] Iarrobino A., Kanev V., The length of a homogeneous form, determinantal loci of catalecticants and Gorenstein algebras, Preprint, North-Eastern Univ., Boston, 1998

[18] Alexander J., Hirschowitz A., “Polynomial interpolation in several variables”, J. Algebraic Geom., 4:1 (1995), 201–222 | MR | Zbl