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manuscripta mathematica

, Volume 54, Issue 3, pp 349–359 | Cite as

Connectedness properties of polynomial maps between affine spaces

  • Gerhard Angermüller
Article

Abstract

Let f:Am→An be a polynomial map between affine spaces. We give some sufficient conditions for the connectedness of the difference kernel of f and relate this to the Jacobian Conjecture.

Keywords

Number Theory Algebraic Geometry Topological Group Affine Space Connectedness Property 
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References

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    S. ABHYANKAR and L. A. RUBEL: Every difference polynomial has a connected zero-set, J. Indian Math. Soc.43 (1979) 69–78Google Scholar
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    H. BASS, E. H. CONNELL, D. L. WRIGHT: The Jacobian Conjecture: Reduction of degree and formal expansion of the inverse, Bull.A.M.S.7 (1982) 287–330Google Scholar
  3. [3]
    W. FULTON and J. HANSEN: A connectedness theorem for projective varieties, with applications to intersections and singularities of mappings. Annals Math.110 (1979) 159–166Google Scholar
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    W. FULTON and R. LAZARSFELD: Connectivity and its applications in Algebraic Geometry, in: Algebraic Geometry, Proceedings of the Midwest Algebraic Geometry Conference 1980, Lecture Notes in Mathematics862 (1981) 26–92Google Scholar
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    L. A. RUBEL, A. SCHINZEL, H. TVERBERG: On difference polynomials and hereditarily irreducible polynomials, J. Number Theory12 (1980) 230–235Google Scholar

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • Gerhard Angermüller
    • 1
  1. 1.Mathematisches Institut der Universität Erlangen-NürnbergErlangenBundesrepublik Deutschland

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