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We classify all quadratic homogeneous polynomial maps $H$ and Keller maps ofthe form $x + H$, for which $rk J H = 3$, over a field $K$ of arbitrarycharacteristic. In particular, we show that such a Keller map (up to a squarepart if $char K=2$) is a tame automorphism.

Quadratic homogeneous polynomial maps $H$ and Keller maps $x+H$ with $rk JH=3$