A note on the Jacobian condition and two points at infinity

Authors:
James H. McKay and Stuart Sui Sheng Wang

Journal:
Proc. Amer. Math. Soc. **111** (1991), 35-43

MSC:
Primary 14E07; Secondary 13B10, 14E20

DOI:
https://doi.org/10.1090/S0002-9939-1991-1034887-3

MathSciNet review:
1034887

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Abstract: If two polynomials and satisfy the Jacobian condition and the Newton polygon of has an edge of negative slope, then the sum of terms of along this edge has at most two distinct irreducible factors and their exponents must be different. Moreover, the slope is either a (negative) integer and the edge touches the -axis or a (negative) Egyptian fraction and the edge touches the -axis. Furthermore, there is an elementary automorphism which reduces the size of the Newton polygon.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1991-1034887-3

Keywords:
Jacobian condition (Jacobian hypothesis),
Newton polygon,
points at infinity

Article copyright:
© Copyright 1991
American Mathematical Society