Annali dell’Università di Ferrara

, Volume 36, Issue 1, pp 159–174 | Cite as

On monomialk-Buchsbaum curves inP r

  • Mario Fiorentini
  • Le Tuan Hoa


This paper is deveted to the study of projective monomialk-Buchsbaum curves C. First, using the theory of affine semigroup rings, we give a criterion forC to bek-Buchsbaum. Then we give some lower and upper bounds for the numberk c such thatC is strictlyk c-Buchsbaum. For some classes of monomial curves we can computek C explicity.


Complete Intersection Numerical Semigroup Space Curf Semigroup Ring Minimal Free Resolution 
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. [1]
    E. Ballico,On the order of projective curves, Rend. Cir. Mat. Palermo, Serie II,38 (1989), pp. 155–160.zbMATHGoogle Scholar
  2. [2]
    H. Bresinsky,Monomial Buchsbaum ideals in P r, Manuscripta Math.,47 (1984), pp. 105–132.zbMATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    H. Bresinsky,Minimal free resolutions of monomial curves in P k3, Linear Alg. Appl.,59 (1984), pp. 121–129.zbMATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    H. BresinskyC. Huneke,Liaison of monomial curves in P 3, J. Reine Angew. Math.365 (1986), pp. 33–66.zbMATHMathSciNetGoogle Scholar
  5. [5]
    H. BresinskyRenschuch,Basisbestimmung Veronesescher Projektionsideale mit allgemeiner Nullstelle (t 0m, t0m−r t1r, t0m−r t1s, t1/m), Math. Nachr.,96 (1980), pp. 257–269.CrossRefMathSciNetGoogle Scholar
  6. [6]
    H. BresinskyP. SchenzelW. Vogel,On liaison, arithmetically Buchsbaum curves and monomial curves in P 3. J. Alg.,86 (1984), pp. 283–301.zbMATHCrossRefMathSciNetGoogle Scholar
  7. [7]
    D. EisenbudS. Goto,Linear free resolutions and minimal multiplicity, J. Alg.,88 (1984), pp. 89–133.zbMATHCrossRefMathSciNetGoogle Scholar
  8. [8]
    Ph. Ellia,Ordres et cohomogie des fibres de rang deux sur l'espace projectif, Preprint, Nice,170 (1987).Google Scholar
  9. [9]
    M. FiorentiniA. T. Lascu,Projective embeddings and linkage, Rend. Sem. Mat. Fis. Milano,57 (1987), pp. 161–182.zbMATHMathSciNetCrossRefGoogle Scholar
  10. [10]
    F. Gaeta,A geometrical characterization of smooth k-Buchsbaum curves, to appear in Springer Lecture Notes in Math.Google Scholar
  11. [11]
    A. V. GeramitaP. MarosciaW. Vogel,A note on arithmetically Buchsbaum curves in P 3. Matematiche (Catania),40, fasc. I–II (1985), pp. 21–28.MathSciNetGoogle Scholar
  12. [12]
    S. Giuffrida—R. Maggioni,On the Rao module of a curve lying on a smooth cubic surface in P 3,-II, preprint CIMPA, Nice (1990).Google Scholar
  13. [13]
    S. GotoN. SuzukiK. Watanabe,On affine semigroup rings, Japan J. Math,2 (1976), pp. 1–12.MathSciNetGoogle Scholar
  14. [14]
    W. Gröbner,Über Veronesesche Varietäten und deren Projectionen, Arch. Math.,16 (1965), pp. 257–264.zbMATHCrossRefMathSciNetGoogle Scholar
  15. [15]
    L. GrusonL. LazarfeldC. Peskine,On a theorem of Castelnuovo and the equations defining space curves, Invent. Math.,72 (1983), pp. 491–506.zbMATHCrossRefMathSciNetGoogle Scholar
  16. [16]
    L. T. Hoa,Algorithmetical aspects of the problem of classifying multi-projections of Veronesian varieties, Manuscripta Math.,63 (1989), pp. 317–331.zbMATHCrossRefMathSciNetGoogle Scholar
  17. [17]
    L. T. Hoa,k-Buchsbaum monomial curves in P 3. Manuscripta Math. (to appear).Google Scholar
  18. [18]
    L. T. Hoa—R.M. Miro-Roig—W. Vogel,On numerical invariants of locally Cohen-Macaulay schemes in P n, prepring M.P.I. (1990).Google Scholar
  19. [19]
    J. Kästner,Zu einem Problem von H. Bresinsky über monomiale Buchsbaum Kurven, Manuscripta Math.,54 (1985), pp. 197–204.CrossRefMathSciNetGoogle Scholar
  20. [20]
    J. MiglioreR. M. Miro-Roig,On k-Buchsbaum curves in P 3, Commun. Alg.,18 (8) (1990), pp. 2403–2422.zbMATHCrossRefMathSciNetGoogle Scholar
  21. [21]
    R. M. Miro-Roig, Some remarks on quasi-complete intersection space curves, Ann. Univ. Ferrara, Sez. VII, Sci. Mat.,34 (1988), pp. 237–245.MathSciNetGoogle Scholar
  22. [22]
    C. PeskineL. Szpiro,Liaison des varietés algébriques Invent. Math.,26 (1973), pp. 271–302.CrossRefMathSciNetGoogle Scholar
  23. [23]
    R. Pao,Liaison among curves in P k3, Invent. Math.,50 (1979), pp. 205–217.Google Scholar
  24. [24]
    J. StückradW. Vogel,Buchsbaum rings and applications, Springer, Berlin, Heidelberg, New-York (1986).Google Scholar
  25. [25]
    N. V. Trung,Classification of the double projections of Veronese varieties, J. Math. Kyoto Univ.,22 (1983), pp. 567–581.zbMATHGoogle Scholar
  26. [26]
    N. V. Trung,Degree bound for the defining equations of projective monomial curves, Acta Math. Vietnam,9 (1984), pp. 157–163.zbMATHMathSciNetGoogle Scholar
  27. [27]
    N. V. Trung,Projections of one-dimensional Veronese Varieties, Math. Nachr.,118 (1984), pp. 47–67.zbMATHCrossRefMathSciNetGoogle Scholar
  28. [28]
    N. V. TrungL. T. Hoa,Affine semigroups and Cohen-Macaulay rings generated by monomials, Trans. Amer. Math. Soc.,298 (1986), pp. 145–167.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Università degli Studi di Ferrara 1990

Authors and Affiliations

  • Mario Fiorentini
    • 1
  • Le Tuan Hoa
    • 2
  1. 1.Depart. Math. Univ. FerraraFerraraItalia
  2. 2.Institute of Math.HanoiVietnam

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