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On the Cohen-Macaulay property of A[pt, p(2)t2] for space monomial curves

Published online by Cambridge University Press:  22 January 2016

Yukio Nakamura*
Affiliation:
Department of Mathematics, Tokyo Metropolitan University, Minami Ohsawa 1-1 Hachioji, Tokyo, 192-03, Japan
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Let A = k[X, Y, Z] and k[U] be polynomial rings over a field k and let l, m and n be positive integers with gcd(l, m, n) = 1. We denote by p the defining ideal of the space monomial curve x = ul, y = um, and z = un.

Type
Research Article
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1993

References

[1] Buchsbaum, D. A. and Eisenbud, D., Algebra structures for finite free resolutions and some structure theorem for ideals of codimension 3, Amer. J. Math., 99 (1977), 447485.Google Scholar
[2] Goto, S., Nishida, K. and Shimoda, Y., The Gorensteinness of symbolic Rees algebras for space curves, J. Math. Soc. Japan, 43 (1991), 465481.Google Scholar
[3] Goto, S., Nishida, K. and Shimoda, Y., The Gorensteinness of the symbolic blow-ups for certain space monomial curves, to appear in Trans. Amer. Math. Soc. Google Scholar
[4] Goto, S., Nishida, K. and Shimoda, Y., Topics on symbolic Rees algebras for space monomial curves, Nagoya Math. J., 124 (1991), 99132.Google Scholar
[5] Herzog, J., Generators and relations of abelian semigroups and semigroups ring, Manuscripta Math., 3 (1970), 175193.CrossRefGoogle Scholar
[6] Herzog, J. and Kunz, E., Der kanonische Modul eines Cohen-Macaulay-Rings, Lecture notes in Math., 238, Springer-Verlag.Google Scholar
[7] Herzog, J. and Ulrich, B., Self-linked curve singularities, Nagoya Math. J., 120 (1990), 129153.Google Scholar
[8] Kamoi, Y., Defining ideal of a Cohen-Macaulay semigroup ring, Comm. Alg., 20 (1992), 3163>3189.Google Scholar
[9] Kunz, E., Almost complete intersections are not Gorenstein ring, J. Alg., 28 (1974), 111115.CrossRefGoogle Scholar
[10] Morimoto, M. and Goto, S., Non-Cohen-Macaulay symbolic blow-ups for space monomial curves, to appear in Proc. Amer. Math. Soc.Google Scholar
[11] Morales, M. and Simis, A., The second symbolic power of an arithmetically Cohen-Macaulay monomial curves in P3 , to appear in Comm. Alg.Google Scholar
[12] Schenzel, P., Examples of Noetherian symbolic blow-up rings, Rev. Roumaine Math. Pures Appl, 33 (1988), 4, 375383.Google Scholar
[13] Robbiano, L. and Valla, G., Some curves in P3 are set-theoretic complete intersections, in Lecture Notes in Math., 997, Springer-Verlag.Google Scholar
[14] Valla, G., On the symmetric and Rees algebras of an ideal, Manuscripta Math., 30, (1980), 239255.Google Scholar
[15] Valla, G., On the set-theoretic complete intersection, in Lecture Notes in Math., 1092, Springer-Verlag.Google Scholar
[16] Zariski, O. and Samuel, P., Commutative Algebra, Vol. II. Van Nostrand 1960.CrossRefGoogle Scholar