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On the vanishing and the positivity of intersection multiplicities over local rings with small non complete intersection loci

Published online by Cambridge University Press:  22 January 2016

Kazuhiko Kurano
Kazuhiko Kurano*
Affiliation:
Department of Mathematics, Tokyo Metropolitan University, Minami-Ohsawa 1-1, Hachioji, Tokyo, 192-03, Japan e-mail address: [email protected]
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Throughout this paper A is a commutative Noetherian ring of dimension d with the maximal ideal m and we assume that there exists a regular local ring S such that A is a homomorphic image of S, i.e., A = S/I for some ideal I of S. Furthermore we assume that A is equi-dimensional, i.e., dim A = dim A/ for any minimal prime ideal of A. We put

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Type
Research Article
Information
Nagoya Mathematical Journal , Volume 136 , December 1994 , pp. 133 - 155
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1994

References

[1] Artin, M., Algebraic approximation of structures over complete local rings, Publ. Math. I.H.E.S., 36 (1969) 23–58.Google Scholar
[2] Buchsbaum, D. A. and Eisenbud, D., What makes a complex exact?, J. Algebra, 25 (1973), 259–268.Google Scholar
[3] Dutta, S. P., Frobenius and multiplicities, J. Algebra, 85 (1983), 424–448.CrossRefGoogle Scholar
[4] Dutta, S. P., A special case of positivity, Proc. Amer. Math. Soc., 103 (1988), 344–346.Google Scholar
[5] Dutta, S. P., Hochster, M. and MacLaughlin, J. E., Modules of finite projective dimension with negative intersection multiplicities, Invent. Math., 79 (1985), 253 — 291.Google Scholar
[6] Fulton, W., Intersection Theory, Springer-Verlag, Berlin, New York, 1984.Google Scholar
[7] Gillet, H. and Soulé, C., K-théorie et nullité des multiplicites d’intersection, C. R. Acad. Sci. Paris Ser. I Math., 300 (1985), 71–74.Google Scholar
[8] Hirzebruch, F., Topological methods in algebraic geometry, 1956, Grundlehren der math. Wissenschaften, Vol. 131, Third enlarged edition, Springer-Verlag, 1966.Google Scholar
[9] Hochster, M., Topics in the homological theory of modules over local rings, C. B. M. S. Regional Conference Series in Math., 24. Amer. Math. Soc. Providence, R. I., 1975.Google Scholar
[10] Kurano, K., An approach to the characteristic free Dutta multiplicities, J. Math. Soc. Japan, 45 (1993), 369–390.Google Scholar
[11] Nagata, M., Local Rings, Interscience Tracts in Pure and Appl. Math., Wiley, New York, 1962.Google Scholar
[12] Roberts, P., The vanishing of intersection multiplicities and perfect complexes, Bull. Amer. Math. Soc., 13 (1985), 127–130.Google Scholar
[13] Roberts, P., MacRae invariant and the first local chern character, Trans. Amer. Math. Soc., 300 (1987), 583–591.Google Scholar
[14] Roberts, P., Local Chern characters and intersection multiplicities, Proc. of Symposia in Pure Math., 46 (1987), 389–400.CrossRefGoogle Scholar
[15] Roberts, P., Intersection theorems, Commutative algebra, Proc. Microprogram, June 15-July 12, 1987, Math. Sci. Res. Inst. Publ., no. 15, Springer-Verlag, Berlin, Heidelberg, London, Paris, Tokyo, 1989, 417–436.Google Scholar
[16] Roberts, P.. Local Chern classes, multiplicities, and perfect complexes, Société Mathématique de France Mémoire, no. 38 (1989), 145–161.Google Scholar
[17] Serre, J-P., Algèbre locale. Multiplicités, Lect. Note in Math., vol. 11, Springer-Verlag, Berlin, New York, 1965.Google Scholar