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), 3543
MSC:
Primary 14E07; Secondary 13B10, 14E20
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:
http://dx.doi.org/10.1090/S00029939199110348873
PII:
S 00029939(1991)10348873
Keywords:
Jacobian condition (Jacobian hypothesis),
Newton polygon,
points at infinity
Article copyright:
© Copyright 1991
American Mathematical Society
