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- W2950380004 abstract "Abstract A self-map F of an affine space ${bf A}_k^n $ over a field k is said to be a Keller map if F is given by polynomials F 1 , …, F n ∈ k [ X 1 , …, X n ] whose Jacobian determinant lies in $ksetminus {0}$ . We consider char( k ) = 0 and assume, as we may, that the F i s vanish at the origin. In this note, we prove that if F is Keller then its base ideal I F = 〈 F 1 , …, F n 〉 is radical (a finite intersection of maximal ideals in this case). We then conjecture that I F = 〈 X 1 , …, X n 〉, which we show to be equivalent to the classical Jacobian Conjecture. In addition, among other remarks, we observe that every complex Keller map admits a well-defined multidimensional global residue function." @default.
- W2950380004 created "2019-06-27" @default.
- W2950380004 creator A5052983024 @default.
- W2950380004 date "2019-06-11" @default.
- W2950380004 modified "2023-10-18" @default.
- W2950380004 title "An ideal-theoretic approach to Keller maps" @default.
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