Advertisement

manuscripta mathematica

, Volume 63, Issue 3, pp 317–331 | Cite as

Algorithmetical aspects of the problem of classifying multi-projections of Veronesian varieties

  • Le Tuan Hoa
Article

Abstract

It is shown that in order to check the arithmetical Cohen-Macaulayness or Buchsbaumness of projections of Veronesian varieties one only needs finitely many operations. A practical criterion for a class of projections of one-dimensional Veronesian varieties to have these properties is given. As a consequence, we obtain an upper bound for the difference between the Buchsbaum invariant and the length of the semigroup ideal for the Buchsbaum projections.

Keywords

Number Theory Algebraic Geometry Topological Group Practical Criterion Semigroup Ideal 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    H. Bresinsky, Monomial Buchsbaum ideals in Pr. manuscripta math. 47(1984), 105–132Google Scholar
  2. [2]
    S. Goto, On the Cohen-Macaulayfication of certain Buchsbaum rings. Nagoya Math. J. 80(1980), 107–116Google Scholar
  3. [3]
    S. Goto, N. Suzuki and K. Watanabe, On affine semigroup rings. Japanese J. Math. 2(1976), 1–12Google Scholar
  4. [4]
    W. Gröbner, Über Veronesesche Varietäten und deren Projectionen. Arch. Math. 16(1965), 257–264Google Scholar
  5. [5]
    L.T. Hoa, Classification of the Triple Projections of Veronese Varieties. Math. Nachr. 128(1986), 185–197Google Scholar
  6. [6]
    M. Hochster, Ring of invariants of tori, Cohen-Macaulay rings generated by monomials and polytopes. Ann. Math. 96(1972), 318–337Google Scholar
  7. [7]
    J. Kästner, Zu einem Problem von H. Bresinsky über monomiale Buchsbaum Kurven. manuscripta math. 54 (1985), 197–204Google Scholar
  8. [8]
    P. Schenzel, On Veronesean embeddings and projections of Veronesean varieties. Arch. Math. 30 (1978), 391–397Google Scholar
  9. [9]
    N.V. Trung, Classification of double projections of Veronese varieties. J. Math. Kyoto Univ. 22(1983), 567–581Google Scholar
  10. [10]
    N.V. Trung, Projections of one-dimensional Veronese varieties. Math. Nachr. 118(1984), 47–67Google Scholar
  11. [11]
    N.V. Trung and L.T. Hoa, Affine semigroups and Cohen-Macaulay rings generated by monomials. Trans. Amer. Math. Soc. 298(1986), 145–167Google Scholar

Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Le Tuan Hoa
    • 1
  1. 1.Sektion MathematikMartin-Luther-UniversitätHalle

Personalised recommendations