Uniqueness of plane embeddings of special curves
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- by Shreeram S. Abhyankar and Avinash Sathaye
- Proc. Amer. Math. Soc. 124 (1996), 1061-1069
- DOI: https://doi.org/10.1090/S0002-9939-96-03254-6
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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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Bibliographic 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