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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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] Masayoshi Nagata, Local rings, Interscience Tracts in Pure and Applied Mathematics, No. 13, Interscience Publishers a division of John Wiley & Sons New York-London, 1962. MR 0155856
  • [3] Oscar Zariski and Pierre Samuel, Commutative algebra. Vol. II, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N. J.-Toronto-London-New York, 1960. MR 0120249

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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