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Polynomial maps with constant Jacobian

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Abstract

It has been long conjectured that ifn polynomialsf 1, …,f n inn variables have a (non-zero) constant Jacobian determinant then every polynomial can be expressed as a polynomial inf 1, …,f n. In this paper, various extra assumptions (particularly whenn=2) are shown to imply the conclusion. These conditions are discussed algebraically and geometrically.

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References

  1. S.S. Abhyankar and T. Moh,Puiseaux expansion and generalized Tschirnhausen transformation I, J. Reine Angew. Math.260 (1973), 47–83.

    MathSciNet  Google Scholar 

  2. S.S. Abhyankar and T. Moh,Puiseaux expansion and generalized Tschirnhausen transformation II, J. Reine Angew. Math.261 (1973) 29–54.

    MathSciNet  Google Scholar 

  3. S.S. Abhyankar and T. Moh, Embeddings of the line in the plane, J. Reine Angew. Math.276 (1975), 148–166.

    MATH  MathSciNet  Google Scholar 

  4. L.A. Campbell,A condition for a polynomial map to be invertible, Math. Ann.205 (1973), 243–248.

    Article  MathSciNet  Google Scholar 

  5. H.W.E. Jung,Über Ganze Birationale Transformationen der Ebene, J. Reine Angew. Math.184 (1942), 161–174.

    MATH  MathSciNet  Google Scholar 

  6. M. Nagata,On the Automorphism Group of k [x, y], Kinokianiya Book Store, Tokyo, 1972.

    Google Scholar 

  7. W. Van der Kulk,On polynomial rings in two variables, Nieuw Arch. Wisk. (3)I (1953), 33–41.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of Maryland, 20742, College Park, MD, USA

    Michael Razar

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  1. Michael Razar
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Razar, M. Polynomial maps with constant Jacobian. Israel J. Math. 32, 97–106 (1979). https://doi.org/10.1007/BF02764906

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  • DOI: https://doi.org/10.1007/BF02764906

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