Polynomial maps in two variables with smoothness on one line |
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| Authors: | Hang Yang |
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| Institution: | School of Mathematics, Jilin University, Changchun, China |
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| Abstract: | Let F be a polynomial map in two variables over the complex field with nonzero constant Jacobian. Abhyankar proved that if F is smooth on generic lines then F is invertible. We sharpen Abhyankar’s result by proving that if F(𝕃) is smooth on one line 𝕃 then F is invertible. Criterion for smoothness of F(𝕃) is also discussed. |
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| Keywords: | D-resultant Jacobian conjecture polynomial map smoothness |
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