manuscripta mathematica

, Volume 91, Issue 1, pp 467–481 | Cite as

The lifting of determinantal prime ideals

  • Ngo Viet Trung


The main results of this paper show that a perfect prime ideal generated by the maximal minors of a matrix has the equality between symbolic and ordinary powers if the ideals generated by the low order minors of the matrix have grade large enough and that any determinantal prime ideal of maximal minors with maximal grade of a matrix of homogenous forms whose 2-minors are homogeneous can be lifted to a prime determinantal ideal having the above equality.


Prime Ideal Local Ring Noetherian Ring Regular Sequence Homogeneous Element 
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  1. [1]
    Achilles, R., Schenzel, P., Vogel, W.:Bemerkungen über normale Flachheit und normale Torsionfreiheit und Anwendungen, Period. Math. Hungaria12 (1981), 49–75.zbMATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    Bruns, W.: The Eisenbud-Evan generalized principal ideal theorem and determinantal ideals, Proc. Amer. Math. Soc.83 (1981), 19–24.zbMATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    Bruns, W., Vetter, U.: Determinantal rings, Lect. Notes Math. 1327, berlin-Heidelberg-New York: Springer 1988.Google Scholar
  4. [4]
    DeConcini, C., Eisenbud, D., Procesi, C.:Young diagrams and determinantal varieties, Invent. Math.56 (1980), 129–165.zbMATHCrossRefMathSciNetGoogle Scholar
  5. [5]
    Eisenbud, D.:Linear sections of determinantal varieties, Amer. J. Math.110 (1988), 541–575.zbMATHCrossRefMathSciNetGoogle Scholar
  6. [6]
    Eisenbud, D., Huneke, C.:Cohen-Macaulay Rees algebras and their specialisation, J. Algebra81 (1983), 202–224.zbMATHCrossRefMathSciNetGoogle Scholar
  7. [7]
    Frauke, S.:Generic determinantal schemes and the smoothability of determinantal schemes of codumension 2, Manuscripta Math.82 (1994) 417–431.zbMATHMathSciNetGoogle Scholar
  8. [8]
    Germaita, A., Migliore, J.C.:Hyperplane sections of a smooth curve in P 3, Comm. Algebra17 (1989), 3129–3164.MathSciNetGoogle Scholar
  9. [9]
    Herrmann, M., Ikeda, S., Orbanz, U.: Multiplicity and blowing-ups, Berlin-Heidelberg-New York: Springer 1988.Google Scholar
  10. [10]
    Herzog, J., Trung, N.V., Valla, G.:Hyperplane sections of reduced irreducible varieties of low codimension, J. Math. Kyoto Univ.33 (1994), 47–72.MathSciNetGoogle Scholar
  11. [11]
    Hochster, M.:Generically perfect modules are strongly generically perfect, Proc. London Math. Soc.23 (1971), 477–488.zbMATHCrossRefMathSciNetGoogle Scholar
  12. [12]
    Hochster, M.:Criteria for the equality of ordinary and symbolic powers of primes, Math. Z.133 (1973), 53–65.zbMATHCrossRefMathSciNetGoogle Scholar
  13. [13]
    Hochster, M.:Properties of Noetherian rings stable under general grade reduction, Arch. Math.24 (1973), 393–396.zbMATHCrossRefMathSciNetGoogle Scholar
  14. [14]
    Hochster, M., Eagon, J.:Cohen-Macaulay rings, invariant theory, and the generic perfection of determinantal loci, Amer. J. Math.93 (1971), 1020–1058.zbMATHCrossRefMathSciNetGoogle Scholar
  15. [15]
    Merle, M., Guisti, M.:Sections des varietés determinantielles par les plans des coordonées, In: Algebraic Geometry, La Rabida 1981, Lect. Notes Math. 961 (1982), 103–119.Google Scholar
  16. [16]
    Trung, N.V.:Über die Übertragung von Ringeigenschaften zwischen R und R[u]/(F), Math. Nachr.92 (1979), 215–229.zbMATHMathSciNetGoogle Scholar
  17. [17]
    Trung, N.V.:On the symbolic powers of determinantal ideals, J. Algebra58 (1979), 361–369.zbMATHCrossRefMathSciNetGoogle Scholar
  18. [18]
    Trung, N.V.:Principal systems of ideals, Acta Math. Vietnamica6 (1981), 239–250.Google Scholar
  19. [19]
    Trung, N.V.:On a certain transitivity of the graded ring associated with an ideal, Proc. Amer. Math. Soc.85 (1982), 489–495.zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 1996

Authors and Affiliations

  • Ngo Viet Trung
    • 1
  1. 1.Institute of MathematicsHanoiVietnam

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