Abstract
In the paper there have been investigated polynomial mappings (P,Q): ℂ2 → ℂ2 in the aspect of the connection between the structure of the jacobian and the coordinates of the mapping. There have been obtained some informations on coefficients of an expansion of the Newton-Puiseux type of one of the coordinates with respect to the other one. Starting from these informations, a theorem is proved stating that if d denotes the degree of the jacobian of the mapping (P,Q), then each of the coordinates P and Q has at most d + 2 zeros at infinity. There have been obtained some equations connecting the homogeneous components of the polynomials P and Q.
Keywords
- Prime Factor
- Prime Number
- Homogeneous Polynomial
- Effective Relation
- Homogeneous Component
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References
S.S. ABHYANKAR, Expansion techniques in algebraic geometry, Tata Institute of Fundamental Research, Bombay 1977.
H. BASS, E.H. CONNEL, and D. WRIGHT, The jacobian conjecture: reduction of degree and formal expansion of the inverse, Bull. of Amer.Mat.Soc. Vol. 7, No. 2, (1982), pp. 287–330.
O.H. KELLER, Ganze Cremona-Transformationen, Monats.Math.Physik 47 (1939), pp.299–306.
A. MAGNUS, Volume-preserving transformations in several complex variables, Proc. Amer. Math. Soc. Vol. 5 (1954), pp. 256–266.
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© 1985 Springer-Verlag
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Charzyński, Z., Chądzyński, J., Skibiński, P. (1985). A Contribution to Keller's jacobian conjecture. In: Ławrynowicz, J. (eds) Seminar on Deformations. Lecture Notes in Mathematics, vol 1165. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076145
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DOI: https://doi.org/10.1007/BFb0076145
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-16050-2
Online ISBN: 978-3-540-39734-2
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