Mathematische Zeitschrift

, Volume 219, Issue 1, pp 187–201 | Cite as

On zero-dimensional subschemes of a complete intersections

  • Ngô Viêt Trung
  • Giuseppe Valla


Prime Ideal Complete Intersection Regular Sequence Hilbert Function Hyperplane Section 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [B]
    Briancon, J.: Sur le degré des relations entre polynomes. C. R. Acad. Sc. Paris 297: 553–556 (1983)zbMATHMathSciNetGoogle Scholar
  2. [BGM]
    Bigatti, A.M., Geramita, A.V., Migliore, J.C.: Geometric consequences of extremal behaviour in a Theorem of Macaulay (Preprint)Google Scholar
  3. [C]
    Castelnuovo, G.: Ricerche di geometria sulle curve algebriche. Zanichelli, Bologna (1937)Google Scholar
  4. [CCD]
    Chiantini, L., Ciliberto, C., Di Gennaro, V.: The genus of projective curves. Duke Math. J. 70: 229–245 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  5. [D]
    Davis, E.D.: Complements to a paper of Dubreil. (Preprint)Google Scholar
  6. [DGM]
    Davis, E.D., Geramita, A.V., Maroscia, P.: Perfect homogeneous ideals: Dubreil’s theorems revisited. Bull. Sc. Math. 108: 143–185 (1984)zbMATHMathSciNetGoogle Scholar
  7. [DGO]
    Davis, E.D., Geramita, A.V., Orecchia, F.: Gorenstein algebras and the Cayley-Bacharach theorem. Proc. A. M. S. 93: 593–597 (1985)zbMATHCrossRefMathSciNetGoogle Scholar
  8. [Du]
    Dubreil, P.: Sur quelques propriétés des systèmes de points dans le plant et des courbes algébraiques. Bull. Soc. Math. France 61: 258–283 (1933)zbMATHMathSciNetGoogle Scholar
  9. [EH]
    Eisenbud, D., Harris, J.: Curves in Projective space. Sem. Mat. Sup. 85, Le Presse de l’Université de Montreal, Montreal (1982)zbMATHGoogle Scholar
  10. [G]
    Geramita, A.: Remarks on the number of generators of some homogeneous ideals. Bull. Sc. Math. 107: 193–207 (1983)zbMATHMathSciNetGoogle Scholar
  11. [GM]
    Geramita, A., Migliore, J.: Hyperplane sections of a smooth curve inP 3. Comm. Algebra 17: 3129–3164 (1989)zbMATHMathSciNetGoogle Scholar
  12. [Go]
    Gotzmann: Eine Bedingung für die Flachheit und das Hilbertpolynom eines graduierten Ringes. Math. Z. 158: 61–70 (1978)zbMATHCrossRefMathSciNetGoogle Scholar
  13. [GP]
    Gruson, L., Peskine, C.: Genre de courbes de l’espace projectif. Lect. Notes in Math. 687: 31–59 (1978)MathSciNetCrossRefGoogle Scholar
  14. [Gr]
    Green, M.: Restrictions of linear series to hyperplanes, and some results of Macaulay and Gotzmann. SLN 1389, Algebraic Curves and Projective Geometry. Proceedings Trento. Berlin Heidelberg New York: Springer-Verlag 1988Google Scholar
  15. [Hi]
    Hibi, T.: Flawless O-sequences and Hilbert Functions of Cohen-Macaulay integral domains. J. Pure Appl. Algebra 60: 245–251 (1989)zbMATHCrossRefMathSciNetGoogle Scholar
  16. [Hn]
    Hartshorne, R.: Stable vector bundles of rank 2. Math. Ann. 238: 229–280 (1978)zbMATHCrossRefMathSciNetGoogle Scholar
  17. [HTV]
    Herzog, J., Trung, N.V., Valla, G.: On hyperplane sections of reduced irreducible varieties of low codimension. J. Math. Kyoto Univ. (to appear)Google Scholar
  18. [M]
    Macaulay, F.S.: Some properties of enumeration in the theory of modular systems. Proc. Lond. Math. Soc. 26: 531–555 (1927)CrossRefGoogle Scholar
  19. [MR]
    Maggioni, R. Ragusa, A.: The Hilbert function of generic plane sections of curves ofP 3. Invent. Math. 91: 253–258 (1988)zbMATHCrossRefMathSciNetGoogle Scholar
  20. [PRP]
    Paxia, G., Raciti, G., Ragusa, A.: Uniform properties and Hilbert functions for points on a smooth quadric. J. Algebra 149: 102–121, (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  21. [R1]
    Raciti, G.: Sulla Funzione di Hilbert di un sottoschema zero-dimensionale diP 3. Ann. Univ. Ferrara 35: 99–112 (1989)zbMATHMathSciNetGoogle Scholar
  22. [R2]
    Raciti, G.: Hilbert Function and geometric properties for a closed zero-dimensional subscheme of a quadricQP 3. Comm. in Alg. 18 3041–3053 (1990)zbMATHMathSciNetGoogle Scholar
  23. [RV]
    Robbiano, L., Valla, G.: On Normal Flatness and Normal Torsion-freeness. J. Algebra 43: 552–560 (1976)zbMATHCrossRefMathSciNetGoogle Scholar
  24. [Sa]
    Sally, J.: Numbers of generators of ideals in local rings. Lect. Notes in Pure and Appl. Math. 35, Marcel Dekker (1978)Google Scholar
  25. [Sau]
    Sauer, T.: Smoothing projectively Cohen-Macaulay space curves. Math. Ann. 272: 83–90 (1985)zbMATHCrossRefMathSciNetGoogle Scholar
  26. [St1]
    Stanley, R.: Hilbert functions of graded algebras. Adv. in Math. 28: 57–83 (1978)zbMATHCrossRefMathSciNetGoogle Scholar
  27. [St2]
    Stanley, R.: On the Hilbert function of a Cohen-Macaulay domain. J. Pure and Appl. Al. 73: 307–314 (1991)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • Ngô Viêt Trung
    • 1
  • Giuseppe Valla
    • 2
  1. 1.Institute of MathematicsHanoiVietnam
  2. 2.Dipartimento di MatematicaUniversità di GenovaGenovaItaly

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