Uniqueness of plane embeddings of special curves

Authors:
Shreeram S. Abhyankar and Avinash Sathaye

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

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Abstract | References | Similar Articles | Additional Information

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.

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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

DOI:
https://doi.org/10.1090/S0002-9939-96-03254-6

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

Article copyright:
© Copyright 1996
American Mathematical Society