Coordinates Arising from Affine Fibrations

We study the question of whether residual coordinates arising from affine fibrations are coordinates. We show that the second Venereau polynomial is a coordinate, and introduce a related class of residual coordinates, called Venereau-type polynomials, and show many of them to be coordinates. We give some partial results towards the Dolgachev-Weisfeiler conjecture in the case of tame strongly residual coordinates