Free affine actions of unipotent groups on Cn

Abstract

We consider free affine actions of unipotent complex algebraic groups on Cn and prove that such actions admit an analytic geometric quotient if their degree is at most 2. Moreover, we classify free affine C2-actions on Cn of degree n - 1 and n - 2. For every n > 4, an action of degree n - 2 appears in the classification whose quotient topology is not Hausdorff.