Isac Heden

We study complex affine G_a-threefolds X with the affine plane A^2 as their algebraic quotient, and which are a principal bundle over the punctured affine plane A^2_*. Changing the point of view, we look for affine extensions of G_a-principal bundles over A^2_* that are obtained by adding an extra fiber to the bundle projection over the origin. It turns out that SL_2 plays a special role, since every G_a-principal bundle can be obtained as a pullback of SL_2. We construct two series of such extensions which generalize the basic extension obtained by adding a zero section to SL_2 viewed as a G_m-principal bundle over P_1 x P_1 minus Delta.