Nagoya Mathematical Journal

Topics on symbolic Rees algebras for space monomial curves

Shiro Goto, Koji Nishida, and Yasuhiro Shimoda

Full-text: Open access

Article information

Source
Nagoya Math. J., Volume 124 (1991), 99-132.

Dates
First available in Project Euclid: 14 June 2005

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1118783019

Mathematical Reviews number (MathSciNet)
MR1142978

Zentralblatt MATH identifier
0739.13001

Subjects
Primary: 13A30: Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics
Secondary: 13C40: Linkage, complete intersections and determinantal ideals [See also 14M06, 14M10, 14M12] 13H10: Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also 14M05] 14H50: Plane and space curves

Citation

Goto, Shiro; Nishida, Koji; Shimoda, Yasuhiro. Topics on symbolic Rees algebras for space monomial curves. Nagoya Math. J. 124 (1991), 99--132. https://projecteuclid.org/euclid.nmj/1118783019


Export citation

References

  • [1] Buchsbaum, D. A. and Eisenbud, D., What makes a complex exact, J. Alg., 25 (1973), 259-268.
  • [2] Buchsbaum, Algebra structures for finite free resolutions and structure theorems for ideals of codimension 3, Amer. J. Math., 99 (1977), 447-485.
  • [3] Burch, L., Codimension and analytic spread, Proc. Camb. Phil. Soc, 72 (1972), 369-373.
  • [4] Goto, S., Herrmann, M., Nishida, K. and Villamayor, 0., On the structure of Noetherian symbolic Rees algebras, manuscripta math., 67 (1990), 197-225.
  • [5] Goto, S., Nishida, K. and Shimoda, Y., The Gorensteinness of symbolic Rees al- gebras for space curves, J. Math. Soc. Japan, 43 (1991), 465-481.
  • [6] Goto, The Gorensteinness of the symbolic blow-ups for certain space monomial curves, to appear in Trans. Amer. Math. Soc.
  • [7] Herzog, J., Generators and relations of abelian semigroups and semigroup rings, manuscripta math., 3 (1970), 175-193.
  • [8] Herzog, J. and Kunz, E., Der kanonische Modul eines Cohen-Macaulay-Rings, Lecture Notes in Math., 238, Springer (1971).
  • [9] Herzog, J. and Ulrich, B., Self-linked curve singularities, Nagoya Math. J., 120 (1990), 129-153.
  • [10] Huckaba, S., Analytic spread modulo an element and symbolic Rees algebras, J. Algebra, 128 (1990), 306-320.
  • [11] Huneke, C, Hubert functions and symbolic powers, Michigan Math. J., 34 (1987), 293-318.
  • [12] Huneke, The primary components of and integral closures of ideals in 3-dimensional regular local rings, Math. Ann., 275 (1986), 617-635.
  • [13] Huneke, On the finite generation of symbolic blow-ups, Math. Z., 179 (1982), 465-472.
  • [14] McAdam, S., Asymptotic prime divisors, Lecture Notes in Math., 1023, Springer (1983).
  • [15] Morimoto, M. and Goto, S., Non-Cohen-Macaulay symbolic blow-ups for space monomial curves, to appear in Proc. Amer. Math. Soc.
  • [16] Peskine, C. and Szpiro, L., Liaison des varietes algebliques. I., Invent Math., 26 (1975), 271-302.
  • [17] Sally, J., Numbers of generators of ideals in local rings, Lecture Notes in Pure and Appl. Math., 35, Marcel Dekker (1978).
  • [18] Serre, J. P., Algebre Locale Multiplicites (third edition), Lecture Notes in Math., 11, Springer Verlag (1975).
  • [19] Schenzel, P., Examples of Noetherian symbolic blow-up rings, Rev. Roumaine Math. Pures Appl., 33 (1988), 4, 375-383.
  • [20] Simis, A. and Trung, N. V., The divisor class group of ordinary and symbolic blow-ups, Math. Z., 198 (1988), 479-491.
  • [21] Valla, G., On the symmetric and Rees algebras of an ideal, manuscripta math., 30 (1980), 239-255. Department of Mathematics School of Science and Technology Meiji University Higashimita, Tama-kn Kawasaki-shi 21U Japan