On a Question of Yosef Stein

Hanspeter Kraft ()
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Hanspeter Kraft: Universität Basel, Mathematisches Institut

A chapter in Automorphisms of Affine Spaces, 1995, pp 225-229 from Springer

Abstract: Abstract During the Curaçao Conference on “Polynomial Automorphisms of Affine Space” Yosef Stein posed the following problem. Let φ = (f,g): ℂ2 → ℂ2 be a polynomial map (f,g ∈ ℂ[x,y]) and denote by σ:ℂ[x,y] → ℂ[x,y] the corresponding algebra homomorphism, i.e., σ(x) = f, σ(y) = g. Assume that $$Jac\alpha : = \det \left( {\begin{array}{*{20}{c}} {\frac{{\partial f}}{{\partial x}}} & {\frac{{\partial f}}{{\partial y}}} \\ {\frac{{\partial g}}{{\partial x}}} & {\frac{{\partial g}}{{\partial y}}} \\ \end{array} } \right) = 1$$ and that φ is not an isomorphism.

Keywords: Euler Characteristic; Finite Order; Algebra Homomorphism; Unique Fixed Point; Affine Space (search for similar items in EconPapers)
Date: 1995
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DOI: 10.1007/978-94-015-8555-2_16

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