Transformation Groups

, Volume 12, Issue 1, pp 137-151

First online:

Free affine actions of unipotent groups on Cn

  • A. PuttmannAffiliated withFakultat fur Mathematik, Ruhr-Universitat Bochum, 44780 Email author 

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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.