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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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Uniqueness of plane embeddings of special curves
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by Shreeram S. Abhyankar and Avinash Sathaye PDF
Proc. Amer. Math. Soc. 124 (1996), 1061-1069 Request permission

Abstract:

For a family of special affine plane curves, it is shown that their embeddings in the affine plane are unique up to automorphisms of the affine plane. Examples are also given for which the embedding is not unique. We also discuss the Lin-Zaidenberg estimate of the number of singular points of an irreducible curve in terms of its rank. Formulas concerning the rank of the curve lead to an alternate simpler version of the proof of the Epimorphism Theorem.
References
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Additional Information
  • Shreeram S. Abhyankar
  • Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
  • Email: ram@cs.purdue.edu
  • Avinash Sathaye
  • Affiliation: Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506
  • Email: sohum@math.uky.edu
  • Received by editor(s): October 24, 1994
  • Additional Notes: This work was partly supported by NSF grant DMS 91–01424 and NSA grant MDA 904–95–H–1008.
  • Communicated by: Wolmer V. Vasconcelos
  • © Copyright 1996 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 124 (1996), 1061-1069
  • MSC (1991): Primary 13B10, 13B25, 14C40, 14H20
  • DOI: https://doi.org/10.1090/S0002-9939-96-03254-6
  • MathSciNet review: 1317027