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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Polynomial expansion
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by Shreeram S. Abhyankar PDF
Proc. Amer. Math. Soc. 126 (1998), 1583-1596 Request permission

Abstract:

The idea of initial form is refined into the concept of polyform. This can be used to streamline desingularization.
References
  • Shreeram Shankar Abhyankar, Resolution of singularities of embedded algebraic surfaces, Pure and Applied Mathematics, Vol. 24, Academic Press, New York-London, 1966. MR 0217069
  • Shreeram S. Abhyankar, Desingularization of plane curves, Singularities, Part 1 (Arcata, Calif., 1981) Proc. Sympos. Pure Math., vol. 40, Amer. Math. Soc., Providence, RI, 1983, pp. 1–45. MR 713043
  • Shreeram S. Abhyankar, Weighted expansions for canonical desingularization, Lecture Notes in Mathematics, vol. 910, Springer-Verlag, Berlin-New York, 1982. With a foreword by U. Orbanz. MR 653634
  • Shreeram S. Abhyankar, Good points of a hypersurface, Adv. in Math. 68 (1988), no. 2, 87–256. MR 934366, DOI 10.1016/0001-8708(88)90015-1
  • Bhaskaracharya, Beejaganit, 1150.
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  • 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
  • Shreeram S. Abhyankar
  • Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
  • Email: ram@cs.purdue.edu
  • Received by editor(s): July 29, 1996
  • Received by editor(s) in revised form: November 8, 1996
  • Additional Notes: This work was partly supported by the Deutsche Forschungsgemeinschaft and the National Security Agency.

  • Dedicated: Dedicated to Herbert Popp for his Sixtieth Birthday
  • Communicated by: Wolmer V. Vasconcelos
  • © Copyright 1998 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 126 (1998), 1583-1596
  • MSC (1991): Primary 12F10, 14H30, 20D06, 20E22
  • DOI: https://doi.org/10.1090/S0002-9939-98-04183-5
  • MathSciNet review: 1443142