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Affine Geometry
Jacobian Conjecture ★★★
Author(s): Keller
Conjecture Let
be a field of characteristic zero. A collection
of polynomials in variables
defines an automorphism of
if and only if the Jacobian matrix is a nonzero constant.
![$ k $](/files/tex/c450c3185f7285cfa0b88d3a903c54f7df601201.png)
![$ f_1,\ldots,f_n $](/files/tex/c4cbeed48b0c6ce2a6294c75261da86958fb7393.png)
![$ x_1,\ldots,x_n $](/files/tex/aaa29ecce30762f5fa8655c6d5de69088530a526.png)
![$ k^n $](/files/tex/b2baee4a1dacdb8cbb7880c33194a814fe14947b.png)
Keywords: Affine Geometry; Automorphisms; Polynomials
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