A1-fibrations on affine threefolds

An A1-fibration on an algebraic surface is well understood and plays an important role in the classification of open algebraic surfaces. We consider A1-fibrations on higher-dimensional affine algebraic varieties, mostly in the case of affine threefolds and extend the results known in the case of surfaces. Special attention is paid to degenerate fibers of A1-fibrations and singularities of the quotient surface by a Ga-action. We distinguish the quotient morphism by a Ga-action from an A1-fibration. Ga-actions will give more information on the A1-fibration induced by the actions.