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Seven Lectures on Polynomial Automorphisms

In: Automorphisms of Affine Spaces

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  • Arno van den Essen

    (University of Nijmegen, Department of Mathematics)

Abstract

Throughout these lectures we use the following notation and terminology: ℕ:= {1, 2, 3,...}, ℕ̅ = ℕ ∪ {0}, ℚ = the rational numbers, ℝ:= the real numbers and ℂ:= the complex numbers. Furthermore k will denote an arbitrary field and F = (F 1, ..., F n): k n → k n a polynomial map i.e. a map of the form $$\left( {{{x}_{1}}, \ldots ,{{x}_{n}}} \right) \mapsto \left( {{{F}_{1}}\left( {{{x}_{1}}, \ldots ,{{x}_{n}}} \right), \ldots ,{{F}_{n}}\left( {{{x}_{1}}, \ldots ,{{x}_{n}}} \right)} \right),$$ where each F i belongs to the polynomial ring k[X]: = k[X 1, ..., X n ].

Suggested Citation

  • Arno van den Essen, 1995. "Seven Lectures on Polynomial Automorphisms," Springer Books, in: Arno van den Essen (ed.), Automorphisms of Affine Spaces, pages 3-39, Springer.
    • Handle: RePEc:spr:sprchp:978-94-015-8555-2_1
    DOI: 10.1007/978-94-015-8555-2_1
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