Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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
MathSciNet review: 1034887
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Abstract: If two polynomials $ F$ and $ G$ satisfy the Jacobian condition and the Newton polygon of $ F$ has an edge of negative slope, then the sum of terms of $ F$ 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 $ y$-axis or a (negative) Egyptian fraction and the edge touches the $ x$-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/S0002-9939-1991-1034887-3
Keywords: Jacobian condition (Jacobian hypothesis), Newton polygon, points at infinity
Article copyright: © Copyright 1991 American Mathematical Society