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Proceedings of the American Mathematical Society

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The local Hilbert function of a pair of plane curves


Author: S. C. Kothari
Journal: Proc. Amer. Math. Soc. 72 (1978), 439-442
MSC: Primary 14H20; Secondary 13H10
DOI: https://doi.org/10.1090/S0002-9939-1978-0506283-X
MathSciNet review: 0506283
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Abstract: Let R be the local ring of a pair of plane curves at a point. In this paper it is proved that the Hilbert function of such a ring changes by at most one at each stage, and it is essentially nonincreasing.


References [Enhancements On Off] (What's this?)

  • [1] L. Berzolari, Allgemeine Theorie der Hoheren Ebenen Algebraischen Kurven, Encyklopadie der Mathematischen Wissenschaften IIIC4, 1932.
  • [2] M. Nagata, Local rings, Interscience, New York, 1962. MR 0155856 (27:5790)
  • [3] O. Zariski and P. Samuel, Commutative algebra, Vol. II, Van Nostrand, Princeton, N. J., 1962. MR 0120249 (22:11006)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0506283-X
Keywords: Hilbert function, initial forms, initial ideal
Article copyright: © Copyright 1978 American Mathematical Society

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