Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-26T07:29:55.707Z Has data issue: false hasContentIssue false
  • English
  • Français

Rees rings and form rings of almost complete intersections

Published online by Cambridge University Press:  22 January 2016

Markus Brodmann
Markus Brodmann*
Affiliation:
Forschungsinstitut für Mathematik, ETH-Zentrum — CH-8092 Zürich
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Recently different authors have studied the conormal modules I/I2 of almost complete intersections in local Gorenstein rings (c. t. Aoyama [1], Herzog [8], Kunz [13], Matsuoka [16]). An essential tool in these papers is the theory of canonical modules and the fact that these modules are easy to handle in the case of almost complete intersections.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 88 , December 1982 , pp. 1 - 16
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1982

References

[ 1 ] Aoyama, Y., A remark on almost complete intersections, Manuscripta Math., 22 (1977), 225–228.CrossRefGoogle Scholar
[ 2 ] Brodmann, M., Asymptotic stability of Ass (M/InM), Proc. Amer. Math. Soc. 74, no.1 (1979), 16–18.Google Scholar
[ 3 ] Brodmann, M., On the asymptotic nature of the analytic spread, Math. Proc. Cambridge Phil. Soc, 86 (1979), 35–39.CrossRefGoogle Scholar
[ 4 ] Brodmann, M., Finiteness of ideal Transforms, J. Algebra, 63, no. 1 (1980), 162–185.CrossRefGoogle Scholar
[ 5 ] Cowsik, R. C. and Nori, L., On the fibres of blowing up, J. Indian Math. Soc, 40 (1976), 217–222.Google Scholar
[ 6 ] Goto, S., On the Rees algebras of the powers of an ideal generated by a regular sequence, Proceedings of the Institute of Natural Sciences, College of Humanities and Sciences, Nihon University, 13 (1978), 9–11.Google Scholar
[ 7 ] Eisenbud, D., Herrmann, M. and Vogel, W., Remarks on regular sequences, Nagoya Math. J., 67 (1977), 177–180.CrossRefGoogle Scholar
[ 8 ] Herzog, J., Ein Cohen-Macaulay Kriterium mit Anwendung auf den Konormalenmodul und den Differentialmodul, Math. Z., 163 (1978), 149–162.CrossRefGoogle Scholar
[ 9 ] Herzog, J. and Kunz, E., Der kanonische Modul eines Cohen-Macaulay-Ringes, Lect. Notes in Math., 238 (1971).CrossRefGoogle Scholar
[10] Hochster, M., Criteria for equality of ordinary and symbolic powers of primes, Math. Z., 133 (1973), 54–65.CrossRefGoogle Scholar
[11] Hochster, M. and Eagon, J. A., Cohen-Macaulay rings invariant theory and the generic perfection of determinantal loci, Amer. J. Math., 93 (1971), 1020–1058.CrossRefGoogle Scholar
[12] Hochster, M. and Jr.Ratliff, L. J., Five theorems on Macaulay rings, Pacific J. Math., 44 (1973), 147–172.CrossRefGoogle Scholar
[13] Kunz, E., The conormal module of an almost complete intersection, Proc. Amer. Math. Soc, 73 (1979), 15–21.CrossRefGoogle Scholar
[14] Peskine, C. and Szpiro, L., Liaison des variétés algébriques, Invent. Math., 26 (1974), 271–302.CrossRefGoogle Scholar
[15] Matsumura, H., Commutative Algebra, W. A. Benjamin, New York (1970).Google Scholar
[16] Matsuoka, T., On almost complete intersections, Manuscripta Math., 22 (1977), 329–340.CrossRefGoogle Scholar
[17] Murthy, M. P., A note on the “Primbasissatz”, Arch. Math., XII (1961), 425–428.CrossRefGoogle Scholar
[18] Nastold, H.-J., Zum Primbasissatz in regularen lokalen Ringen, Arch. Math., XII (1961), 30–33.CrossRefGoogle Scholar
[19] Rees, D., The grade of an ideal or module, Proc. Cambridge Phil. Soc, 53 (1957), 28–42.CrossRefGoogle Scholar
[20] Robbiano, L., An algebraic property of P1 X PN comm. Algebra, 7 (1978), 641–655.Google Scholar
[21] Robbiano, L. and Valla, G., On normal flatness and normal torsion-freeness, J. Algebra, 53 (1976), 552–560.CrossRefGoogle Scholar
[22] Valla, G., Certain graded algebras are always Cohen-Macaulay, J. Algebra, 42 (1976), 537–548.CrossRefGoogle Scholar
[23] Huneke, C., On the symmetric and Rees-Algebra of an ideal generated by a d-sequence, J. Algebra, 62 (1980), 268–275.CrossRefGoogle Scholar
[24] Huneke, C., The Theory of d-Sequences and powers of ideals, Adv. in Math., to appear.Google Scholar