Abstract
An A 1 -fibration on an algebraic surface is well understood and plays an important role in the classification of open algebraic surfaces. We consider A 1 -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 A 1 -fibrations and singularities of the quotient surface by a G a -action. We distinguish the quotient morphism by a G a -action from an A 1 -fibration. G a -actions will give more information on the A 1 -fibration induced by the actions.
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