The Gorensteinness of symbolic Rees algebras for space curves

Shiro GOTO; Koji NISHIDA; Yasuhiro SHIMODA

doi:10.2969/jmsj/04330465

Shiro GOTO, Koji NISHIDA, Yasuhiro SHIMODA

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JOURNAL FREE ACCESS

1991 Volume 43 Issue 3 Pages 465-481

DOI https://doi.org/10.2969/jmsj/04330465

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Published: 1991 Received: July 17, 1990 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: AUTHOR Details: Wrong : S. GOTO¹⁾, K. NISHIDA²⁾, Y. SHIMODA³⁾
Right : Shiro GOTO¹⁾, Koji NISHIDA²⁾, Yasuhiro SHIMODA³⁾

Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) N. Bourbaki, Commutative Algebra, Addison-Wesley Publishing Company, 1972.
2) L. Burch, Codimension and analytic spread, Proc. Camb. Phil. Soc., 72 (1972), 369-373.
3) R. C. Cowsik, Symbolic powers and the number of defining equations, Algebra and Its Applications, Lecture Notes in Pure and Appl. Math., 91 (1985), 13-14.
4) S. Eliahou, Symbolic powers of monomial curves, J. Algebra, 117 (1988) , 437-456,
5) S. Goto, M. Herrmann, K. Nishida and O. Villamayor, On the structure of Noetherian symbolic Rees algebras, Manuscripta Math., 67 (1990), 197-225.
6) S. Goto, K. Nishida and Y. Shimoda, The Gorensteinness of the symbolic blow-ups for certain space monomial curves, in preparation.
7) S. Goto and Y. Shimoda, On the Rees algebras of Cohen-Macaulay local rings, Lecture Notes in Pure and Appl. Math., 68(1982), 201-231.
8) S. Goto and K. Watanabe, On graded rings I, J. Math. Soc. Japan, 30(1978), 179-213.
9) J. Herzog, Generators and relations of abelian semigroups and semigroup rings, Manuscripta Math., 3 (1970), 175-193.
10) J. Herzog and B. Ulrich, Self-linked curve singularities, Nagoya Math. J., 120 (1990), 129-153.
11) C. Huneke, On the finite generation of symbolic blow-ups, Math. Z., 179 (1982), 465-472.
12) C. Huneke, Hilbert functions and symbolic powers, Michigan Math. J., 34 (1987), 293-318.
13) S. Huckaba, Symbolic powers of prime ideals with applications to hypersurface rings, Nagoya Math. J., 113 (1989), 161-172.
14) S. Huckaba, Analytic spread modulo an element and symbolic Rees algebras, J. Algebra, 128 (1990), 306-320.
15) S. Ikeda, On the Gorensteinness of Rees algebras over local rings, Nagoya Math. J., 102 (1986), 135-154.
16) D. Katz and L. J. Ratliff, Jr., On the symbolic Rees ring of a primary ideal, Comm. in Algebra, 14 (1986), 959-970.
17) M. P. Murthy, A note on factorial rings, Arch. Math., 15 (1964), 418-420.
18) M. Nagata, On the fourteenth problem of Hilbert, Proc. Internat. Congress Math., 1958, Cambridge Univ. Press, 1960.
19) D. Rees, On a problem of Zariski, Illinois J. Math., 2 (1958), 145-149.
20) P. Roberts, A prime ideal in a polynomial ring whose symbolic blow-up is not Noetherian, Proc. Amer. Math. Soc., 94 (1985), 589-592.
21) P. Schenzel, Examples of Noetherian symbolic blow-up rings, Rev. Roumaine Math. Pures Appl., 33(1988), 4, 375-383.
22) A. Simis and N. V. Trung, The divisor class group of ordinary and symbolic blow-ups, Math. Z., 198 (1988), 479-491.
23) P. Valabrega and G. Valla, Form rings and regular sequences, Nagoya Math. J., 72 (1978), 93-101.

Right : [1] N. Bourbaki, Commutative Algebra, Addison-Wesley Publishing Company, 1972.
[2] L. Burch, Codimension and analytic spread, Proc. Camb. Phil. Soc., 72 (1972), 369-373.
[3] R. C. Cowsik, Symbolic powers and the number of defining equations, Algebra and Its Applications, Lecture Notes in Pure and Appl. Math., 91 (1985), 13-14.
[4] S. Eliahou, Symbolic powers of monomial curves, J. Algebra, 117 (1988), 437-456,
[5] S. Goto, M. Herrmann, K. Nishida and O. Villamayor, On the structure of Noetherian symbolic Rees algebras, Manuscripta Math., 67 (1990), 197-225.
[6] S. Goto, K. Nishida and Y. Shimoda, The Gorensteinness of the symbolic blow-ups for certain space monomial curves, in preparation.
[7] S. Goto and Y. Shimoda, On the Rees algebras of Cohen-Macaulay local rings, Lecture Notes in Pure and Appl. Math., 68 (1982), 201-231.
[8] S. Goto and K. Watanabe, On graded rings I, J. Math. Soc. Japan, 30(1978), 179-213.
[9] J. Herzog, Generators and relations of abelian semigroups and semigroup rings, Manuscripta Math., 3 (1970), 175-193.
[10] J. Herzog and B. Ulrich, Self-linked curve singularities, Nagoya Math. J., 120 (1990), 129-153.
[11] C. Huneke, On the finite generation of symbolic blow-ups, Math. Z., 179 (1982), 465-472.
[12] C. Huneke, Hilbert functions and symbolic powers, Michigan Math. J., 34 (1987), 293-318.
[13] S. Huckaba, Symbolic powers of prime ideals with applications to hypersurface rings, Nagoya Math. J., 113 (1989), 161-172.
[14] S. Huckaba, Analytic spread modulo an element and symbolic Rees algebras, J. Algebra, 128 (1990), 306-320.
[15] S. Ikeda, On the Gorensteinness of Rees algebras over local rings, Nagoya Math. J., 102 (1986), 135-154.
[16] D. Katz and L. J. Ratliff, Jr., On the symbolic Rees ring of a primary ideal, Comm. in Algebra, 14 (1986), 959-970.
[17] M. P. Murthy, A note on factorial rings, Arch. Math., 15 (1964), 418-420.
[18] M. Nagata, On the fourteenth problem of Hilbert, Proc. Internat. Congress Math., 1958, Cambridge Univ. Press, 1960.
[19] D. Rees, On a problem of Zariski, Illinois J. Math., 2 (1958), 145-149.
[20] P. Roberts, A prime ideal in a polynomial ring whose symbolic blow-up is not Noetherian, Proc. Amer. Math. Soc., 94 (1985), 589-592.
[21] P. Schenzel, Examples of Noetherian symbolic blow-up rings, Rev. Roumaine Math. Pures Appl., 33(1988), 4, 375-383.
[22] A. Simis and N. V. Trung, The divisor class group of ordinary and symbolic blow-ups, Math. Z., 198 (1988), 479-491.
[23] P. Valabrega and G. Valla, Form rings and regular sequences, Nagoya Math. J., 72 (1978), 93-101.

Date of correction: October 20, 2006 Reason for correction: - Correction: PDF FILE Details: -

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